No, unless you have glass doors and can see the insides.

Why paint if they are nice wood cabinets? Stained wood is a much more durable finish than paint.

No, leave the insides stain. They are much easier to maintain, than paint is.

Stay with the wood stain. Give them a good clean. Change the hardware, if you want. Change the wall color. Just don't paint the cabs.

No need to paint the insides. If you want colorful or pretty INSIDE, go with shelf paper -- you can run it "up the back" of the inside cabinet too.

I painted my kitchen cabinets in 2016. Did not paint the insides, but I did paint underneath them. Sometimes people forget about that. (It's 10 years later and my cabinets STILL look amazing!)

What is the stain color, and what color are you painting?