She suddenly said she loved me!

A few months ago, a girl I used to work with reached out to me on Facebook and we began chatting. She said she had wanted to speak when we were colleagues but didn’t feel confident enough. I was pleasantly surprised and, as I got to know her better, realised she had feelings for me. I didn’t say anything and agreed to go on a date with her just so I could get to know her better. When we met, she said she was in love with me and wanted to know if I would consider a relationship. I politely told her I was flattered, but that I didn’t even know her as a person and couldn’t agree to something like this without spending some time with her. She said she would give me time, and promptly stopped communicating with me ever since. Did I do something wrong? I can’t reach out to her because she has blocked me on social media.
If she blocked you because you asked for time, you are better off not being in touch because this is clearly someone who doesn’t understand how relationships work. If she reaches out again, think about that last date and decide if you want to risk being with someone so immature.

My girlfriend and I tend to argue about the silliest things but get along when it comes to big issues. Is this a sign that we need to stop being petty, or is this normal in most relationships? We have been together for over a year, so I think we should have understood each other better by now.
It may make sense to not think about other relationships and whether this is normal and accept that no two people are alike. You may understand each other better in a few months, or it may take a lifetime. Arguments are a great way of evolving as a couple, so I suggest you don’t worry about minor disagreements. If you are both happy, nothing else matters.