This is pretty read dependent. In the first situation, you should push with any Ace. The fact that your stack is the shortest at the table by far is a big reason as to why you should be pushing.

The second situation is a little trickier since you have a stack twice as big as UTG. It really depends on how often Button is raising, and with what. If there is a decent chance that he'll fold if you push over him, then you could consider a push. I think the most prudent course might be to let this one go buy and save your chips for when you can open the pot.