Man, no, I'd stay away from Picard to start. It's such a bummer if you jump into it back to back.
Granted, I like it a lot less than most in general, but "hey, it's the guys you remember, just old and cranky now" is not the vibe I'd like to come back. I'll post it separately, but the current show that carries the serialized, free-form tone best is probably Strange New Worlds. There's plenty of time to get into Picard for continuity and nostalgia's sake later.
Yes. This. But only if you have nostalgia for TNG (bonus points for DS9/Voyager).
Do NOT watch Picard seasons 1 or 2. Skip them entirely. I bailed out a few episodes into season 1 and recently picked up season 3. Aside from the first 5 mins of S3E1, you need to know absolutely nothing about the previous seasons. It’s like they suddenly realized that a show called Picard should actually be about Picard and just jettisoned all the nonsense they had been doing beforehand.