I have satin trim inside, latex based. I need to paint over it with satin. Should I prime first then paint the new satin color..?

 

My first thought is to say absolutely not. However there are situations where a prime coat will save time and improves quality. Especially if the color change
is drastic. If I was asked to make black trim turn white I would definitely prime
with a white primer. But in most situations the woodwork is already primed why prime again? Two top coats of your new color should be more than adequate. Maybe only one if you use quality paint, tools and a little tlc.
You should sand a little before you paint. Do a little caulking etc. This little
effort turns "nice" into "wow!".

 

Nope
Only if it's a drastic color change
Usually just a light scuff sanding, then wipe off the dust you made, then paint away