Does the white gate get dirty easily?

Our 2 gates don't look dirty at all but I'm sure they are. My twin 10 month olds put their hands and faces all over them since we installed them 2 months ago. Its screen-like, so you kind of see a bit of what's behind it instead of seeing a solid white panel. So even if it's dirty, it probably just blends in. I totally recommend these gates!

If one side is a stair bannister, do I need to buy an adapter?

It depends. The Stair Banister Kit allows you to mount the brackets to a surface so you can avoid screwing into your banister post. If your banister Post is round, it also gives you a flat surface to attach the mounting brackets.

Cant a baby just climb under this gate?

Our 1 yr old grandson did after he saw our dogs (small breed) do it. This was when set in a 52" wide passage. It would be very hard to do on a 36" doorway. It wasn't an easy crawl for him but he made it. I immediately returned it ( wish they would have repaired the holes it created ) and no questions asked refunded me. I ended up getting a solid swinging gate that collapsed to a shorter length when opened.