If a Vanara wears boots and or gloves does this impact their climb speed?
Can a Vanara even wear boots, or would they wear two pairs of gloves?
The Climb rules say you need to use both hands but say nothing about gloves or the feet, so no, it doesn't matter.
Vanara are described as having "handlike feet capable of well-articulated movements", but there are no mechanics for this in the actual writeup, so it's up to the GM to decide. Personally, I'd allow a Vanara to wear and gain the benefits of boots as normal, both for balance reasons and because there's no rule saying otherwise. I'd also allow custom-made boots to cosmetically appear as gloves, but regular off-the-shelf gloves wouldn't fit on their feet, for balance reasons. They'd be limited to the normal "boots" wondrous item properties until I took a long hard look at the possible interactions with other items. Different magical effects are usually tied to specific slots on the body for a reason, and tinkering with that can lead to shenanigans.