Taking off when you mount is a behavioral issue. When you get on her, bring her back to a halt as soon as you can and then make her stand for several minutes before you go to work.
As for her outside the ring behavior, that sounds to me like she is herdbound.
"Be a best friend, tell the truth, and overuse I love you
Go to work, do your best, don't outsmart your common sense
Never let your prayin knees get lazy
And love like crazy"