I’m worried that he blows hot and cold!

I have been dating a guy who exhibits periods of extreme affection followed by complete lack of interest in me. I don’t know if this is a behavioural trait, but it worries me because it makes me feel unstable in this relationship. I am sometimes so excited to be with him that I want to introduce him to everyone in my life and, at other times, I dread it because he may just ignore me when I’m with friends. The saddest thing is how oblivious he seems to be about this side of his personality. When he’s happy, everything is fine, and he doesn’t remember how badly he has been treating me. I don’t want to end this relationship if he’s unwell, but I can’t think of any way to be more secure in it either. What should I do?
It’s possible that he has some issues that need to be addressed by a professional, especially if he can’t recall his behaviour towards you. You deserve to feel secure in a relationship because it can’t evolve without that basic requirement. If he cares about you and genuinely wants to be with you, neither of you have an option but to call out this behaviour, get him to acknowledge it, and then seek external help if he needs it. Without that intervention, this relationship will stagnate after a point because you will simply tire of him blowing hot and cold.

My girlfriend used to like another guy before we began dating and recently admitted than she only went out with me because he was in a relationship at the time. She says she loves me now and isn’t interested in him anymore, but I don’t know if she means it. How will I know if she’s lying?
She’s with you, not him, and has told you how she feels. If you don’t trust her, or believe what she says, you won’t have a relationship for much longer irrespective of whether she’s being honest or lying to you.