If a half-elf where to disguise himself with a disguise kit, would he be able to change his appearance enough to pass as a full human among humans, or as a full elf among elves? I'm assuming the character is trained in deception.
Almost certainly, but ask your DM.
The rules for disguising yourself are not as clear-cut in 5e as they were in previous editions. The description of the Disguise Kit just says that it contains:
cosmetics, hair dye, and small props lets you create disguises that change your physical appearance
That's not very specific. In addition, two of the stats mention disguises as something that the stat does. Under Intelligence:
Pull together a disguise to pass as a city guard
Under Deception, which is under Charisma:
pass yourself off in a disguise,
So basically, what you're specifically able to do with a disguise kit is going to vary from campaign to campaign.
In general, I would be very surprised if a particular DM didn't allow you to disguise yourself as a similarly-sized humanoid with similar features. There's not much difference, visually, between Humans, Half-elves, and Elves, so members of those races should almost certainly be able to disguise themselves as those three. Your GM might allow you to disguise yourself as a more different similarly-sized humanoid, like a Dragonborn, Half-orc, or Tiefling, but that is much less assured. You probably can't disguise yourself as a much shorter race, like a Halfling or Gnome.
Broadly speaking, the only way that D&D 5e handles making a particular opposed check harder or easier is through advantage and disadvantage. Since spotting a disguise is an opposed check (DMG 238), your DM should apply advantage or disadvantage to a particularly easy or hard disguise.
For example, if you're a half-elf disguising yourself as an elf, but not any specific elf, that's probably a really easy disguise, and you should get advantage. However, if you're a half-elf trying to disguise yourself as a tiefling, you're going to have some problems vis-a-vis horns and tail. You'd probably have disadvantage on that roll.
There are three points, I think, when trying to pass for another:
- Your disguise must be good, if you have proficiency with the disguise kit, you are allowed to add your proficiency to your ability checks (+2 at level 1);
- You have to be convincing, this means having to roll your ability checks (Deception check uses Charisma); if that roll fails, then your disguised did not work;
- Also, someone may specifically say that they are suspicious and get a check to see whether they can see through your disguise (Investigation check, using Intelligence, see Hag's Illusory Appearance ability as an example.)
Each time you try something new*, you need to roll an ability check to make sure your disguise does not get discovered. This can make it difficult to go in disguise for days on.
If you try to deceive a large number of people, unless they cannot see you too closely, it becomes even more difficult. Any one of them could potentially discover your disguise.
According to RAW, there does not seem to be any specific limits other than the fact that you cannot make yourself look shorter or thinner, for example. Taller, fatter, different skin, etc. is certainly all part of the disguise kit. Of course, a Tiefling's tail could be a problem.
Now, to answer your question specifically, I think that you could offer either advantage or a bonus (i.e. +5) to an Half-Elf to disguise himself as an Elf or a Human. After all, the differences are small. This is assuming the character does not try to look like a specific person, just himself as a slightly different race. Although the Half-Elf may be a bit fat for an Elf.
Note, however, that RAW does not generally include such edge cases.
- "something new" — this is difficult to define. If you are actively trying to gather information, for example, it certainly requires additional checks. If you are just being yourself, it is probably that you do not need an extra check. As the DM, you should be able to sense when a new check is required. Especially, a new check should be required for each person that meets you. Someone walking by may be given a check, depending on whether you are quiet/discrete or doing something making you quite visible.
Yes, that's what the disguise kit is for. To take on another identity. You could even pass off for a dragon born with a disguise kit so long as you didn't have to prove it beyond superficial appearance.
You pretty much just can't change your size or your general humanoid appearance. (I am including Dragon born as humanoid I this particular regard being roughly shaped as a largish human)