[RPG] What kind of creature is a pre-Medusa

This is actually a really interesting inconsistency.

According to d20SRD.org...

Each character within range of a gaze attack must attempt a saving throw (which can be a Fortitude or Will save) each round at the beginning of his turn.

You could interpret this to mean that the monster with the higher initiative actually has the disadvantage! Since they rolled a higher initiative, they have to roll or divert their eyes first, which implies they may either die or be not-looking come their enemy's turn, which would affect their gaze attack.

Under these circumstances, I think one has to remember that different turns during the same round are supposed to happen concurrently-ish. I think the emphasis isn't on "at the beginning of his turn" as much as it is on "each round". Making the roll "at the beginning of his turn" seems more like an organizational issue - everyone rolling at the start of the round or on the gazer's turn would slow the game down.

As such, even if the first monster dies or turns to stone or diverts their eyes, the other monster should still have to - at the beginning of the round - roll in some way to 'resist' the other's gaze attack.

Example

A beholder and a medusa walk into a bar and roll initiative. The medusa rolls higher and goes first; at the start of its turn it rolls against the beholder's gaze attack, fails and horrifically turns into skittles.

The beholder still has to roll against the medusa's gaze attack; rolls, fails and turns into funk. Combat is over.

The bartender says something witty about the medusa being ugly and beauty being in the eyes of the beholder. WOKA WOKA WOKA!

If we're going with a strict reading, then if you're seeing the medusa's eyes from beyond its range, then you -- the remote viewer -- do not need to make a saving throw.

When a creature that can see the medusa's eyes starts its turn within 30 feet of the medusa, the medusa can force it to make a DC 14 Constitution saving throw if the medusa isn't incapacitated and can see the creature.

Your familiar will need to make a save, of course, if they are within 30ft of the medusa.

If you are within 30ft of the medusa and use your familiar to see, and you see the medusa's eyes, then it depends on the final clause of that rule: if the medusa isn't incapacitated and can see the creature.

Let's imagine you are a resource-depleted familiar-owner hiding from the medusa in an abandoned building. She is only 25ft away from you, but is unaware of your location and cannot see you due to being in total cover from a stack of crates. Then, you look through your familiar's eyes (a spider) to scout the area, but end up looking straight into her eyes.

In the above scenario, you do not make the saving throw, but your familiar does. It would potentially be a traumatizing event though, being in the mind of a creature as it is being petrified.

Otherwise, if you had failed your Stealth check and the medusa actually can see you, and then you scout via your familiar and end up looking into her eyes through the familiar, then yes you will need to make a saving throw.

Strictly speaking, as long as the four conditions are met, you have to make a saving throw.

1. can see the medusa's eyes
2. starts its turn within 30 feet of the medusa
3. the medusa isn't incapacitated
4. the medusa [...] can see the creature

It doesn't matter where your sight comes from as the first condition is not "that can see the medusa's eyes through its own eyes".

I'm reminded of spells such as Misty Step, which allow you to teleport to any unoccupied space you can see within 30ft of you (even if you're seeing through the eyes of your familiar).

As for the case of controlling another creature, that depends on how you are "controlling" them. If it is through Dominate Monster, for example, then only the creature you have controlled makes the save.

But more likely, you're asking about Magic Jar. If you are possessing the body of another creature in this way (your soul leaves your body and steals the body of another living creature), then from the wording of this particular spell, your soul and the possessed creature's body are considered as one creature. You -- the possessor -- must make the saving throw using the stats of the possessed body. If you fail the save, the body you are possessing becomes petrified. If that body also dies, your soul may leave that dead body and go elsewhere.

As for should your original body be petrified along with the possessed body, that depends on if your true body is within 30ft of the medusa. If it is, then you must also make a saving throw with your actual stats.