Advice for a first timer restoring an old radiogram

Hi,

I'm a total noob trying out my first project.

It's an old radiogram (I picked up 2 for $25!) and I've just jumped right in but am now in need of some guidance.

I've removed the damaged veneer from the top ( I figured I can replace this area and it wont look too bad ).

I've sanded back the panels but am a bit stuck now.

So here are my questions....

Can someone help me identify the veneer, I'm thinking walnut? and with that in mind point me in the direction of somewhere i can get some more to fix the top area of the piece.

Second, what is best to use to stick-down lifting veneer? there are a couple of places where it is lifting just a bit ( not enough to warrant total removal ) and I'm not sure what to do.

Here are some pics to help...

I depending on the age it might have been stuck down by hide glue. Which would require the same type of glue to fix as modern and old glue do not mix / stick. I am not exactly sure how to test this but thinking that it can be tested via applying heat and if it comes off then it was hide glue.

I am sure someone with a lot more experience will come along to give better direction.

With the modern glue then it can be applied via a syringe under where the veneer has lifted.