Who do you usually share juicy gossip with?

With whom do you usually share juicy gossip ? ( Formal )

Are both correct?

Question

Who do you usually share juicy gossip with?

With whom do you usually share juicy gossip ?  ( Formal )

Are both correct?

Answer

The first is wrong. You need to say "whom".  Even though you end the sentence with "with", you are using "who" as the object of the preposition "with", and that is an error.

Answer

Yes, they are both correct…
But
Some very strict grammarians avoid ending sentences with a preposition (like with). However this is not something you really to worry about unless you are doing something like giving a speech or writing a dissertation.