I and my boyfriend with our son lived together for 2 years; however, we broke up a year ago. Now, I and my son are living with my parents. My ex does not communicate with me and instead he calls my mom or my sister to ask about our son. There was one time that we talked and he told me to move on and find someone else. He also told me that he hopes that I learned from our relationship. Does this mean that he already moved on?

Yes, it sounds like he has. If it matters to you, it usually indicates that you haven't.

Yes, it is time for you to do the same.

Yes he has moved on and so should you.

Why are you still focused on him? Have you moved on? Focus on you.

After a year, you should not even care if he has or has not moved on. You need to focus on YOU. You are not getting back with him, get over it and move on. He is doing the right thing, not dealing with you directly, he calls your parents which is what is the best thing to do.

But yes most likely he has a new girlfriend, may even be living with someone by now.
But it is none of your business what he is doing.

I am concerned why he does not come and take the child home with him some of the time.

Also have you filed for child support ?