Pretty much all of the questions you ask there don't have rules for them, so it's a matter for the GM. There aren't really rules for creatures as inventory items more generally: a GM might be well within his rights to say simply 'you can't do that'.
>What if I forego the holes entirely and rely on the "bond senses" summoner ability?
You don't have line of effect, so this doesn't work.
For the invisibility thing, I'd probably rule it as "While you're in the backpack, you count as part of the other character. As soon as you leave, you break invisibility. If you cast something or do something that breaks invisibility while in the backpack, it breaks it for both of you."
For the box... I'm not sure; probably have concealment both ways, or the box might interfere with somatic components of your spells. Also, expect to have enemies come smash the box up.
Blackmane is right: ask your GM.
If you were my player, you might be able to do what you're asking, however you should expect to get picked on by anything that can get you for being cheesy.
Eg you might be counted as helpless while inside your box...
Lets pretend I have a gnome witch with a tiny sized familiar in my backpack and I cast invisibility on myself. Familiar is invisible too, right?
No, but it is inside of the backpack which is concealed from sight. The creature does not have invisibility cast on it, but being inside of a object that is benefiting allows it to also benefit. If it leaves the backpack it is no longer invisible.
It just like invisibility says:
Items dropped or put down by an invisible creature become visible; items picked up disappear if tucked into the clothing or pouches worn by the creature. Light, however, never becomes invisible, although a source of light can become so (thus, the effect is that of a light with no visible source). Any part of an item that the subject carries but that extends more than 10 feet from it becomes visible.
Also if I cast reduce person on myself in the same situation, the familiar is equally reduced in size until it leaves the bag, right?
This again is wonky. As a GM, I would let this work as long as the familiar remained inside your bag, but not outside. Technically it shouldn't work because reduce person only affects humanoids and the familiar is not equipment worn or carried. If you tried to abuse the combination somehow, as a GM I'm going to invoke this technicality to tell you it doesn't work.
Also, please not there is no "poking it's head out" it's either inside {and can do nothing effectively) or it's outside.
Well... what if I have my familiar in the gnome's backpack and cast reduce person, climb into my medium sized summoner friend's backpack who casts enlarge person on his large sized humanoid eidolon, then climbs into ITS backpack... and casts invisibility on the eidolon?
You have a bunch of entities stacked like nesting dolls, but those inside of things can't really do much unless they get outside of things and lose the magical effects. You don't have line of sight or line of effect to anything.
The only way this really works to be beneficial is if a GM lets players get away with "peeking" out. Which he shouldn't because that is where the game breaks down. Letting players do this is just abuse of the game rules, where you are being generous in the first place.
Bonus questions! If I have a large sized quadruped creature(I'm thinking eidolon for buffing purposes, but can be any) and I strap a small specially designed sized box to it's back with a chair and small holes for vision can I cast spells with full concealment? What if I forego the holes entirely and rely on the "bond senses" summoner ability?
Nope, see previous statement about peeking.
Lets pretend I have a gnome witch with a tiny sized familiar in my backpack and I cast invisibility on myself. Familiar is invisible too, right?
For the time that the familiar is in the backpack, yes. However, once it leaves the backpack, it does to remain invisible unless you share spells with it (which has it's own effect).
Also if I cast reduce person on myself in the same situation, the familiar is equally reduced in size until it leaves the bag, right?
No. The spell effect is one humanoid. So, unless you share spell with your familiar, it remains the same size, potentially breaking the backpack it is in.
Well... what if I have my familiar in the gnome's backpack and cast reduce person, climb into my medium sized summoner friend's backpack who casts enlarge person on his large sized humanoid eidolon, then climbs into ITS backpack... and casts invisibility on the eidolon?
None of the reduces/enlarges effect the person in the backpack or inside multiple backpacks. You (the gnome) nor the familiar is considered to be equipment.
Bonus questions! If I have a large sized quadruped creature(I'm thinking eidolon for buffing purposes, but can be any) and I strap a small specially designed sized box to it's back with a chair and small holes for vision can I cast spells with full concealment? What if I forego the holes entirely and rely on the "bond senses" summoner ability?What if I take a huge sized winged eidolon and I put a seat/strap system on it's back and use it like an airship?
You would have to make concentration checks for each spell cast, due to being "mounted" or "onboard a ship".
Being inside a box prevents spellcasting. It will prevent the free movement needed to cast spells. You will have line of sight with the holes in the box or with the bond senses, however, you would not have line of effect, even if you could cast spells.
