A CR 5 enemy (40 xp, trivial threat) dies and immediately comes back as a CR 7 enemy (80 xp, moderate threat). Would this encounter as a whole be 120 exp and Severe? A little weaker, since they don't fight both enemies at the same time? Or two separate encounters?
This is effectively two back-to-back encounters. The same as if a new creature runs into the room after the first one dies.
Basically for encounter balance there are benefits and drawbacks. The drawbacks are universal: The party doesn't have any time to rest and recover focus points or HP. The benefits only show up if the party is using temporary buffs - like spells such as Bless, Stoneskin, or Resist Energy - or consumables that have similar short duration. The point being that those buffs are still active.
Barbarians are another special case. If you have the death of the first phase enemy end Rage, they won't be able to use Rage during the second phase. That will likely be a huge problem for a Barbarian character.
A CR 7 necromancer (80 xp) with 4 CR1 lackeys (10 xp each) = 120 xp total, Severe Threat. The lackeys are intended to die almost immediately so the boss can use animate dead spell to bring them back, casting it as a 4th level spell (to get a CR3 Wight), then 3rd level spell (to get a CR2 Ghast), then 2nd level spell (to get a CR1 ghoul). How do I even calculate this? Since the necromancer is using spells readily available to him, do I even add the additional creatures count as additional XP to the encounter? If so, would the same concept apply if any spell caster summons some kind of ally (the additional ally = additional xp to the encounter budget)?
Not sure if I've missed this in the rules, but I've been looking and can't find anything, so I appreciate the help!
I vaguely remember something about creatures that summon other creatures don't change their own CR rating - but I am thinking that this is edition confusion with Starfinder.
For PF2, the Animate Dead spell gives the summoned undead creature the Summoned trait, which means that it has the Minion trait. So the continued existence of the undead creature is consuming actions from the necromancer. So I would likely still not change the CR rating of the enemy even if it is summoning minion creatures.
Also since the undead are summoned, no corpse (nor minions to provide said corpse) is necessary. It's still a cool effect to use an available corpse, but technically you can't (w/o GM's permission, which of course you have). And yes, summoned creatures do not increase the difficulty or XP since they are the power of the summoner and not full creatures in their own right. Not that you technically need to use the spell; you could create a faux ability which resembles Animate Dead, but which is just an excuse to have the guy's cannon fodder come back as legit monsters (ran as regular and w/ full XP). Or you could create a real ability special for this NPC that mirrors the Create Undead Ritual, yet instantly.
There are other variants available to get whatever (im-)balance you desire including having the necromancer do effectively nothing except spawn undead, the actual threat that needs to be defeated. He's a plot device, perhaps crumpling once the last undead falls.
ETA: Normal summoned creatures cast from slots aren't a significant threat, and are hardly worth the casting compared to an AoE blast (et al).
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And as noted, the effects of linked battles depends a lot on party composition and its dependence (or lack of same) on Rage, Focus Spells, out-of-combat Medicine, shield repair, and more.
Whether fought back to back, with a lull between, or together it all counts as the same XP. This may seem odd except the difficulty of each varies by party and monster. Together will typically be the most dangerous, duh, but a party that can go nova with buffs, AoEs, and in-combat healing might prefer that.
Since the necromancer is an NPC, you are free to give it a different ability than the spell itself if you want. If you think it makes for a better encounter, definitely go for it - you aren't bound by any rule.
I did a similar thing for the final encounter of an adventure meant as an introduction to PF2e. Three level 4 PCs versus a level 7 necromancer cleric and her two ogre henchmen. I gave the necromancer a three-action ability that animated a homebrewn zombie ogre monster from one of the corpses (or a zombie PC... but she didn't have the chance to use it), without the minion trait, and took away some of her spell slots to compensate. The fight was intended to be tough (a 50/50 in my mind), and it ended up just fine.
Many years ago during a Kingdoms of Kalimar campaign under Dungeons & Dragons 3rd Edition rules, we encountered a housecat sitting atop a treasure chest in a room in an abandoned keep. We knew it could not be a normal cat, since no-one had fed it for decades, but we were too soft-hearted to murder a cat in cold blood. Nevertheless, we were searching for a McGuffin and had to look in the chest it guarded.
So we pulled a bedroll out of our backpack, tried to catch the cat in it, and when we finally pinned it, we stuffed it, bedroll and all, into another chest that we had already emptied. We took about 10 damage from claw attacks while wrestling with the cat.
After we left the keep, the GM told us out of character that the cat was a Cat of Nine Lives. If we killed it, then it would return to life stronger than before. It would resurrect eight times and the final form would be a magical lion-like cat as strong as the party. Containing the cat alive saved us a world of hurt.
fyrekrest's players might not trigger the 2nd form of their enemy.
A CR 5 enemy (40 xp, trivial threat) dies and immediately comes back as a CR 7 enemy (80 xp, moderate threat). Would this encounter as a whole be 120 exp and Severe? A little weaker, since they don't fight both enemies at the same time? Or two separate encounters?This is effectively two back-to-back encounters. The same as if a new creature runs into the room after the first one dies.
The experience points earned in encounters with a 5th-level enemy and a 7th-level enemy (PF2 uses levels rather than CR) will be 120 xp total regardless of whether the two enemies attacked together, attacked in back-to-back encounters, or attacked in totally separate encounters. The only detail that matters is how hard-pressed the party will be.
A back-to-back encounter would deal less damage than a combined encounter. The party won't have the 7th-level enemy beating on them while they fight the 5th-level and vice versa. But they won't be able to Treat Wounds, Refocus, reset rage and so on between the back-to-back like they could between totally separate encounters. However, barring bad luck, a Trivial-threat encounter won't consume any significant resources, so the following Moderate-threat encounter won't catch the party at any significant disadvantage. For gauging difficulty, treat it is a Trivial-threat encounter followed by a Moderate-threat encounter.
It would be different if the situation were a Moderate-threat encounter back-to-back with a Severe-threat encounter, since Moderate-threat encounters do use up resources.