I think this is a really fun game idea!
For question one, a grabbing animation would probably improve the idea that the player is a claw that needs to grab things. I actually have a suggestion of possibly adding a "drop" feature when you've picked up the object. Normally, claw machines drop a prize down their chute, not manually extend all the way down. Perhaps you can add something like that for when players reach the end goal of grabbing the object and reaching the prize zone to streamline the winning sequence?
For question two, I think the project overall does a very good job at conveying the "grab" verb!