Will small size fit a taller than normal nine-year-old boy?

For a nine year old, a small size should be OK. My hands are not large and I am a grown man but the mediums stretched out and are now are comfortable. They offer free returns so if they are too small you can always exchange them if too small.

Are these water proofed? Says wind proof but not about how it handled being wet.

Nope not water proof. I use them for jogging on cold nights. They work great, as I have bad circulation and my hands are always cold. Not really a snow glove

Are they good for climbing in winter?

I’ve never climbed but these are somewhat thick which makes them very warm. I don’t know if you would be able to get your fingers into small cracks with these. I bought them for outside work outs because I had bad circulation and my hand were always cold and jogging gloves were not warm enough. They do have some really good tackiness on the palms and fingers but, mainly for keeping you warm not really for performance

Can I press buttons with these as if I’m texting or are they to bulky?

They're not super bulky, but it probably will depend on how big your phone and keyboard are. I have found most touch screen gloves (these included) to be less than responsive, so I have found it easier to take my gloves off to text.