Impersonal verbs

The il in these constructions refers to nothing at all, and the three are not interchangeable. Existence takes il y a, weather takes il fait or il pleut, and the clock takes il est. Il y a trois heures does not tell anyone the time; il est trois heures does.

Both are built on valoir, but they answer different questions. Il vaut mieux partir tôt compares the action to an alternative (better than leaving late). Ça vaut la peine d'essayer judges the action against doing nothing at all (worth the effort, full stop).

Il vaut la peine de + infinitive always keeps de, even in the everyday ça-version and even in the negative: ça ne vaut pas la peine de se disputer pour ça. Drop the de and the phrase stops parsing.

English you don't have to means it is optional; French il ne faut pas means it is forbidden. Il ne faut pas oublier is you mustn't forget. To say there's no need, use ce n'est pas la peine or tu n'es pas obligé.

Both mean he is or it is, and what follows decides. A noun with un, le or mon takes c'est: c'est un ami. A job with no article takes il est: il est médecin. So il est médecin but c'est un médecin, both he's a doctor. Il est un ami is the classic slip.