She asks if we can stay friends

I am a 26-year-old guy and my girlfriend of two years says she wants to break up because she doesn’t think she has feelings for me anymore. At the same time, she says she wants something to remember me by and wants to know if we can stay friends. I don’t know how to react because this has come as a shock to me. I didn’t do or say anything to make her feel this way, and had no idea there was a problem in our relationship. The more I think about it, the angrier I become. I don’t think I want to see her again. Am I being too hasty?
This isn’t about haste as much as it is about pain and processing what has happened. If this has come as a shock, the first thing to accept is that your relationship wasn’t as strong as you may have thought it to be. It’s possible that neither of you were communicating as much as you ought to have, which may also explain why her feelings have changed. You can choose to be kind, or end all contact, but this depends upon whether you still want this person in your life. It’s okay to ask for time, and it may be years before you find it within yourself to move past this, but to react in anger doesn’t change anything. If she has decided to end it, she has a right to. It isn’t an easy thing to accept, but you don’t have a choice.

Is this normal to feel upset after being physically intimate with someone? I had sex with a guy after three dates and don’t know if I want to see him anymore.
You should do what you are comfortable with. If you had sex because you wanted to, and it was consensual, you don’t have to be upset with yourself. Accept that you acted upon an instinct that felt right and are now choosing to not see this person anymore. You’re allowed to.