>testing passwords against multiple hashes (at the price of one) is impossible

That's defending against a newly generated rainbow table.

> And it is not possible to see if different entries shares a same password (or to see if they have a different password).

That's repeating the first point with different words! It's defending against a pre-generated table. i.e. a rainbow table.

Timing attacks are not mitigated by salts; they're mitigated by the design of the encryption. You should not rely on salts for this. In fact, if your hash is exposed you should assume your salt is also exposed.

What do salts guard against other than rainbow tables?