My Ex Girlfirend And I Got In Contact, Advice Needed Please?

My ex girlfriend split up with me about 3 months ago. She split up with me after 18 months and it seemed very sudden to me. She used reasons like since her 21st birthday (the week before) she needs to be alone for a while, sort her life out with her career, get her own friends and do stuff spare of the moment. This would have been fair enough but I was never one to stand in her way with any of these things and was willing to help her with any of these. She also said that she thought we were heading to something that wasn’t there anymore but a couple of weeks before she mentioned marriage and moving in together and a couple of days before she said she loved me.
I had a feeling there was another reason why she split up with me suddenly so I checked her e-mails as she gave me her passwords before. I felt terrible for doing this but I needed to know. I found a couple of e-mails to her ex (who cheated on her with her best friend about 2 years before me), the e-mails said miss you, and he’d sent one back staying miss you too, I hate monday mornings after our weekends together. This was 2 weeks after we split. I know they met up just after she said she needed some space for a few days but I don’t know if anything happened or is happening. But to other friends, she said her lifes a mess. I do not do this anymore and I will never do it again I hate myself for doing it.
The last 3 months have been hell for me, I love her to pieces and i’ve missed her so much its unreal, I can’t get her out of my mind and I think of her everyday. People told me to just move on and its not that easy, she does still owe me abit of money for a holiday but I was prepared to cut my losses. I maintained no contact for 2 months but last week, her gran died. I felt like I needed to contact her because she was very ill when we split up. I just said I heard about your loss and my thoughts are with your family. She thanked me and left it at that. Then a few days later it was my birthday and she sent me a text saying happy birthday x and I just replyed saying thanks. And then she sent a message saying Have I got anything planned for this year? I replyed with a few things like starting a degree and going on a skiing trip and asked the question back to her. She replyed saying her grans funeral next week and got a few job interviews. We sent a couple more texts to each other and I showed her abit of sympathy towards her gran and said well done with the interviews but I haven’t heard anything since. I’m pretty confused about the whole situation and not sure what to do next. I don’t know why she contacted me after this time, if it was to make the peace or she how I react to her.
I still have strong feelings for her and wish I was still with her but I don’t want to come across like I’m weak or a doormat or anything, but also if she wants to give it another try then I don’t want to act like i’m not interested. I think so far I seemed stong in her eyes and i’ve acted like i’ve moved on but i’m from that. Should I try and get back with her and if so how?
Thanks, advice will be appreciated.