Is there a way to display the uTorrent ETA on my screen?

Yes, there is. On the bar where it says Name, Size, Done etc. right click. Then select ETA from the menu that appears.

Is there a way for it to show up when I hover my mouse over the icon and the download speed shows up? It’s usually minimized.

If you right-click on a torrent, go to the Advanced sub-menu and select “Show download bar”. (I’m not at my own PC right now. I think those names are right, they may be something else though, but it’s something along those lines)
It’ll give you a draggable always-on-top bar that shows a progress bar, down/up speeds, and ETA.

@Sarcasm Awesome dude! Thanks!