I assumed that Mari sort of grew up around Evangelions, like having a family member being part of Seele Euro- essentially Shinji or Asuka if they grew up with normal people (as opposed to any cast member of Evangelion). Seele Euro noticed her aptitude, and started to train her. There's precedent for this in Rebuild, as that's how Asuka is implied to be have chosen.
This also implies that she hasn't actually piloted an Eva before Unit 05. At the very most, she had used training simulations, similar to what Shinji uses in 1.0. All of her knowledge about running an Eva are theoretical. Her comments after her ejection from Unit 05 sort of reflect this line of thought:
Syncing with an Eva is even more brutal than they warned me. Well, I'm alive, so it's all good.
Now comes the problem of her knowing what Beast-Mode is/does. To be honest, any guess on the matter would be reaching far. My personal belief is that she was simply told that Evangelions could intentionally go berserk, but it was probably a bad idea to use it.
I really wanted to agree with Seele00TextOnly that she's older than she looks. I really did. She made a good, solid argument with facts proving her point. However, most of the facts she posted were reaches (not that mine aren't), that my mind didn't jump to. I'm not arguing she's wrong, merely that I don't see the vague facts the same way.
Just my two cents.