Yes you can. You'll want to be sure to use the correct SATA power cable. Here's one that works: http://www.microsatacables.com/15-pin-sata-female-to-female-power-cable/
Keep in mind that in that case you won't be able to attach a SATA drive and still have the case closed. The taller NUC case (coming out this month) is designed to allow for an internal SSD, but the smaller case doesn't.
I hope this helps.
It's unlikely it would be able to fit. The NUC is made to be as small as possible and that means the case is a very tight fight. Also, if you did manage to fit it, you'd probably run into heating issues. The SATA port is really meant to be used in the taller NUC case or an after-market case. The reason it's there in the smaller case is that the same board is used.
The performance difference going from the i3 to the i5 depends on what you're doing with it. If you're browsing the web or doing word processing, for example, you won't see much of a difference. But if you're playing games or doing relatively CPU-heavy tasks the difference is noticeable. The big jump I noticed was in graphics performance. The i3 uses the Intel 4400 HD GPU which is no slouch. But the i5 uses the Intel 5000 HD GPU and it makes a difference.