If my opponent attempts to do a break away can I probability the roll? Same question towards Break Away-Running shot?

Yes, you can on both instances. Sometimes they may even have a higher breakaway roll because of their leapclimp, hypersonic, or plasticity, but maybe you're feeling lucky and think you can get them to roll a 1, which in every breakaway instance is an auto-fail, then by all means, make em reroll.

Yay, that makes my Kuriboh's Plasticity even happier with Hiro's Shadow Scout :D

Dear OP, I'll use your post to ask a related question, if you don't mind:

If I have Runnig Shot (and I'm a Sniper), a try do break away, may I still shot if I fail to break away?

Same question for Charge :O

No. Regardless of circumstances, whenever you fail a breakaway roll your action *immediately* ends.

Ok, thank you!