My opinion on the matter, whether they made out or had sex or even cuddled, what does it matter? She still cheated. Sucks she didn't come out and tell you the truth. The details with cheating don't matter. What matters is that she made a bad choice. If you do forgive her, you can't bring that up anymore. That's the role you have to play. No one on here can tell you whether you can trust her or not. You're the only one that knows that for sure.
The whole her going out at night or going to lunch with a friend, that's another risk you take by taking her back but at the same time, she needs to realize that in order for you to move on from that, she will need to live her life a different way when it comes to that. If she truly loves you and wants to be forgiven, that shouldn't be a problem for her.
You'd be lucky to find any cheater who would come out and tell you exactly what happened when not being pressured to do so. I've been on both ends of that. It sucks to admit and it's a shameful process.
My advice, get to the root of the problem as to why she did what she did. My opinion, no one just goes out and cheats to get theirs. They do it because there is something in their history or mentally wrong with them that makes them do those things. Best of luck!
Whether you like it or not, we (as a society) have developed certain social mores. One of those is the expectation of fidelity within a serious romantic relationship. Sorry, it may be contrary to biology, but that's the way it is. But nobody is bound by this. Millions of people get around this by not committing themselves to one other person. If you can't be monogamous, fine. But you owe it to your partner to be honest. Maybe that spells the end of the relationship, but IMO, it's better than having to be deceitful for the duration.
Do you guys think it's cheating if it's a teacher and student?
I've never felt so lost.
Your Mileage May Vary
I is disappoint.