I have problems landing dive rolls without eating grass or not connecting my roll at the end. 

I had a problem with this one too.

I used to do the roll halfway, but then land on my back.

Get a running start, then jump out, extending your arms, and go into a parkour roll. 

Here is the most important part:

Tuck into a ball.  I didn't realize that I wasn't doing this.  Then just allow the roll to finish and get up and keep running.

The dive roll has a lot more momentum than the normal roll, so tucking into a ball is extremely important.