Yeah, illusions can be tricky to deal with depending on the GM and how creative the players are. The first thing I'd suggest is to get familiar with the types of illusions and their limitations in the CRB. The "image" line of spells are figments.
Figment: A figment spell creates a false sensation. Those who perceive the figment perceive the same thing, not their own slightly different versions of the figment. It is not a personalized mental impression. Figments cannot make something seem to be something else. A figment that includes audible effects cannot duplicate intelligible speech unless the spell description specifically says it can. If intelligible speech is possible, it must be in a language you can speak. If you try to duplicate a language you cannot speak, the figment produces gibberish. Likewise, you cannot make a visual copy of something unless you know what it looks like (or copy another sense exactly unless you have experienced it).Because figments and glamers are unreal, they cannot produce real effects the way that other types of illusions can. Figments and glamers cannot cause damage to objects or creatures, support weight, provide nutrition, or provide protection from the elements. Consequently, these spells are useful for confounding foes, but useless for attacking them directly.
And what happens on saves vs illusions
Saving Throws and Illusions (Disbelief): Creatures encountering an illusion usually do not receive saving throws to recognize it as illusory until they study it carefully or interact with it in some fashion.A successful saving throw against an illusion reveals it to be false, but a figment or phantasm remains as a translucent outline.
A failed saving throw indicates that a character fails to notice something is amiss. A character faced with proof that an illusion isn't real needs no saving throw. If any viewer successfully disbelieves an illusion and communicates this fact to others, each such viewer gains a saving throw with a +4 bonus.
What "interact with" has been debated since the 3.5 days, though most seem to take it as the character must use some action to investigate it (usually a standard action).
So for your examples (and again, expect table variation because illusion spells really depend on the interpretation of the GM, but here's my take):
A.) The lion (or creature) does not need to make a will save unless it interacts with the wall in some way. This might fool creatures with animal intelligence or lower and get them to turn away, but if they have other senses such as scent or tremor sense that might cause them to sense the party on the other side they might just as easily interact with the illusion. More intelligent creatures that see the spell being cast might try to interact with it as soon as the wall appears to make sure if it's real or not (magic can do a lot of things). In either case, once they interact with it, they can make a save. However, if given proof that it is an illusion (such as their hand passing through the wall), they automatically disbelieve.
B.) I'm not familiar with Tangible Image, but with Shadow Conjuration it would seem plausible since shadow illusion spells conjure semi-real material that can affect the Material plane. Having someone create an object and then having others fail the save to disbelieve it means they think it is real enough and can interact with it. Maybe someone else has insight on this one.
C.) Nope. See above. Figments cannot cause damage. Though for role play purposes they might think they are burning, but no actual damage is done
D.) I don't know if there's a definite answer on this one but I would lean towards no. Generally spells shouldn't be able to replicate spells of higher level. Also, in line with the above, "image" spells don't cause any real physical effect as they are not real
A) It stops running and avoids touching the wall. Imagine for a moment, what would you do if you were running down the street with your eyes closed. Then you open them and there, in front of you, is a wall of some kind and you're about to run into it face first. What would you do? Try to crash through it? Of course not. You would stop running and avoid the wall. So will the lion. If the wall was placed so close that it cannot stop, then it will pass harmlessly through the illusory wall and will keep running toward you to have a snack.
B) Figments cannot support weight, so even failing the will save means you cannot walk across the bridge; you just fall through a bridge you thought was real.
C) Figments cannot cause damage to objects or creatures. The wall will seem to give off heat, but the heat won't cause damage (which, if the "victim" expects to be burned but is not, should count as interacting to get another save, with bonuses to the roll since that fire is definitely not realistic at all).
D) Definitely not daylight (which damages vampires and figments cannot cause damage). Maybe it could temporarily blind a vampire (or anyone else) since that technically is not damage, although arguably that blindness might be caused by temporary damage to the eyes which a figment cannot do, so some GMs may not allow it. Even if an argument could be made that by RAW blindness is not damage so it's possible, it still falls under the fact that figments cannot produce real effects (e.g. blindness) so probably is still beyond the capability of a figment.
This should answer most of these kinds of questions:
Figment: A figment spell creates a false sensation. Those who perceive the figment perceive the same thing, not their own slightly different versions of the figment. It is not a personalized mental impression. Figments cannot make something seem to be something else. A figment that includes audible effects cannot duplicate intelligible speech unless the spell description specifically says it can. If intelligible speech is possible, it must be in a language you can speak. If you try to duplicate a language you cannot speak, the figment produces gibberish. Likewise, you cannot make a visual copy of something unless you know what it looks like (or copy another sense exactly unless you have experienced it).
Because figments and glamers are unreal, they cannot produce real effects the way that other types of illusions can. Figments and glamers cannot cause damage to objects or creatures, support weight, provide nutrition, or provide protection from the elements. Consequently, these spells are useful for confounding foes, but useless for attacking them directly.
re: A) the concept seems to be that the spell is cast while the lion is already running/charging, which while combat is supposedly simultaneous actions, effectively we use turns to break it up, and unless you are readying an action to cast during the lion's charge, your casting will happen before the lion even began to charge (or, before it decided to begin charging).
to your question: "which these spells can affect the environment," NONE of them, they don't affect the environment AT ALL, just the victim's PERCEPTIONS, i.e. minds.
figments are illusions that make their victims believe they are perceiving something that is NOT ACTUALLY THERE... thus there is no ACTUAL EFFECT in the real-world. other spells make the victim believe their enemy is an ally when that is not actually the case, that doesn't change the actual fact of the enemy/friend status... nor in this case does it change actual facts re: physical reality.
in this case, believing an illusion of pressure, temperature, light does not mean those have real world effects of those features. a vampire might believe he is seeing "daylight" but there is no real effect because the effect depends on real daylight really affecting the vampire, not what the vampire BELIEVES is happening to them (similar to how Smite Evil depends on the target's real alignment, not what the Paladin believes or perceives via Detect Alignment/Evil). victims may believe you cast a wall of flame that should damage them, but there will be no real damage (which should lead to a new Save at the least, if not sufficient proof to outright disbelieve - if you DO still 'believe' the illusion, you would probably believe the fire is very weak and non-damaging). IF you somehow cast a wall spell DURING the lion's charge (or, say, while it is falling) it MIGHT try to stop (although since there is no 'damage' from running into a wall while charging per RAW, why should any character necessarily stop even vs. a REAL stone wall?), but if you cast it so exactly timed that it couldn't stop (e.g. readied for when the lion starts to enter a square where you target the wall illusion), then the lion would (possibly) "believe" the illusion for a bit, but it wouldn't be damaged and it's movement wouldn't actually be impeded, thus there nothing to impede the charge.
note that there IS illusion magic that DOES replicate damage (even if the damage is at least partly "in the head" of the believing victims), namely Shadow Conjuration/Evocation. that depends on actual rules wording of those spells. other illusion spells that don't have wording to convey damage or other "real" effects upon the victims, DON'T CONVEY THAT DAMAGE/ OTHER EFFECTS, not even "in the head" of the victims (as shadow conj/evo damage works). if your players want to use illusions to do this type of thing, they probably should use Shadow Conjuration/Evocation. (or tone down their expectation of what the Image spells can achieve... which is great enough without giving them the functionality of Shadow Conjuration/Evocation)
also, figment's simulation of senses does not extend to "pain".
you would never feel or believe you had been damaged from and Image,
although you MIGHT still believe the Image is real and potentially dangerous to you.
(e.g. could think you "got off lucky" without actual damage)
P.S. more broadly, have a discussion with your players whether they really want an aggressive manipulation of rules to be standard... because if they do, tell them you can do the exact same thing, and you aren't even obligated to explain every trick to them. tell them they aren't going to win/lose the game based on doing this (or not), so ask them if having rules discussions is really the main attraction for them... if it isn't for you, tell them that, and that you don't want to GM if they want to turn the game into a semi-permanent rules discussion.