I know, these are no official rules but I think it´s worthwhile to consider what Skip Williams wrote on this subject in his Rules of the Game article. According to him you can (even must) assume a different form than your familiar:
You choose a form for yourself and for your familiar or companion. The forms you choose don't have to be the same. In fact, in most cases, they cannot be the same because alter self allows the subject to assume a form of the same type as itself only…
When you share an alter self spell with a familiar or companion, the familiar or companion assumes a form of the same type as its own. While an animal becomes a magical beast upon becoming a familiar, such a creature must assume the form of an animal when sharing an alter self spell. For example, a cat familiar is a magical beast; when it shares an alter self spell, it assumes the form of an animal, such as a dog, a bird or a bat, not the form of a magical beast.
The best advice I have seen on this issue is from Angry GM’s 5 Simple Rules for Dating My Teenaged Skill System (warning: mild, censored swearing of the $^#% variety). That’s written for D&D 4e, but like you say, this is an issue that has perplexed GMs for ages, across a variety of systems.
His answer, which is his rule #2, is very simple:
Only roll if there is a chance of success, a chance of failure, and a risk or cost to failure
You need all three to have a roll. If you have only one or two of the three, or none of the three, there is no reason to roll at all. If there is no chance of success or no chance of failure, the pointlessness of the roll is self-evident,1 but the third point is key here: if there is no reason not to, PCs should and will keep retrying until they succeed (as much as they can succeed). There is no reason to bother wasting time having them actually do so; just assume they do it and move on. Save game time for something more important.
And “it takes longer” is not a risk or cost to failure unless there is a clear and present time crunch being applied to the PCs. If they are under attack, sure, taking more time to search a corpse is risky and/or costly—they risk losing their hp, and possibly lives, by doing it. Likewise if the room is filling with water, the big bad evil guy is chanting in the corner to finish his summoning of a bigger fish, or whatever. But it has to be clear and known to the PCs to give them a reason to rush.
But if they’re just exploring an apparently-abandoned tomb, at their own leisure, there is absolutely no reason in the world for them to not take their time being thorough. It does not improve the game to constantly ask them if they’re going to be. It really does not improve the game to constantly stop and roll and check results and maybe try again when it doesn’t matter. And it also doesn’t improve the game to arbitrarily limit retries; in addition to being unrealistic (rolls represent one attempt, and the whole point of it being randomized is that not every attempt at something will be your best), it also runs into severe goblin dice problems.
Note, however, that this answer assumes implicitly that this kind of thing is a low-value use of limited play time. A whole lot of the trade-offs involved here are made in order to minimize play time spent on this issue. That only makes sense if we agree that this activity is not a major, important, or interesting part of the game. This answer presumes such a playstyle because that is the style that 5e itself seems to espouse—5e continues a progression that largely started with the acquisition of D&D by Wizards of the Coast that focuses more on the epic narrative, the quest, and the characters, than it does on careful dungeon delving, handling preparation and logistics, or on player skills. But even in 5e, that’s not all playstyles—many people play with different styles with different emphases. Particularly since in older editions of D&D, it was presumed that this sort of thing was a very important, interesting part of the game. Said editions wanted to spend more time on this in part because they also emphasized a fairly heavy use of player skill as opposed to character skill—players had to be thorough, players had to think of places to search, and so on. And many people continue to play newer editions that way. If that’s your playstyle, the choices made in this answer would make no sense, since they are emphasizing different things than you are.
- Some will object that choosing not to roll at all gives away information to the players about something’s difficulty. That is, they will argue that not allowing players to roll for something they cannot possibly do tells them explicitly that they cannot do it, when otherwise they could not conclusively know that unless they rolled enough to achieve a natural-20 and still see a failure. Suffice to say that the article acknowledges and addresses this concern—some may not be convinced, but personally I think the discussion on that subject is very well-considered and convinces me, anyway, that this is for the best. The short, short version is that rolling enough to get that natural 20 is a huge waste of time that doesn’t add nearly enough to the game to be worth it.
Best Answer
Finding Found Familiars
Suspicious players could use the spell Detect Evil and Good - a 1st level divination - to at least confirm there is something unusual about an animal, as a familiar summoned by Find Familiar:
And Detect Evil and Good tells you:
A rat which is actually a celestial/fey/fiend is almost certainly a familiar and at least suspicious.
Interrogating Animals
Unfortunately in most respects familiar remain relatively unintelligent beasts without natural capacity for language; none of the default familiar options, including rats, know any languages and the Find Familiar spell doesn't state a general exception to that. The familiar is somehow able to understand, obey and even telepathically commune with its master, but has no means of conversing with anyone else.
The 1st-level spell Speak with Animals allows a character to communicate effectively with beasts. A familiar is not a beast, but a sympathetic GM might rule that a familiar is close enough that the spell works on them. However, a familiar who understands it is opposed to the players would probably not be cooperative, and it's difficult to threaten them since if they "die" the spirit simply disappears back from whence it came and can be summoned by its master again later.
The 2nd-level spell Detect Thoughts is normally a quite useful interrogation technique, but unfortunately it is ineffective when used on creatures with an Intelligence of 3 or less, or that do not understand language - both rule out the rat familiar.
The 3rd-level spell Tongues allows you to give a creature automatic understanding of all language and the ability to be understood by any creature that already knows a language, and it has no restrictions that would prevent you using it on a familiar. It would not be a very bright conversationalist but it should be intelligible. Unfortunately you have the same problem as above that simply being able to converse with the creature does not compel it to actually tell you anything.
However, if you're able to talk to the creature, the 4th-level spell Charm Monster (not part of the basic rules, but essentially identical to Charm Person except that it works on any creature) would convince the familiar that you are its friend and encourage it to be helpful to you, at which point it should be easily persuaded to tell you about its master.
3rd and 4th level spells are probably beyond the reach of a party going through LMoP, though.