How do I handle mom in memory care keeps asking the same questions? Sometimes during the same conversation.

It is fairly typical. You might try to break the loop by saying that you have not seen her for a while or ask her when was the last time she saw her. Stop reminding her that mom died

My mom would start asking if we were going to be late for her doctors’s appointment. We were never late for any appointments. Yet, she was always paranoid about being late.

One time I remember setting the clock back so she could relax about the time! I had to set the one in my car back too.

So, then she would say, “Honey, can we leave early so we won’t be late for my appointment.” Okay, I take her early. Then when we get there she would say, “Why is it taking so long for the doctor to see me?” I said because you wanted to get here early. Then she would say, “Were we early? “Why did we get here this early?”

It is odd how they get stuck on one topic and then forget it then go back to it! It made me think that I was going to lose my mind at times.

I didn’t even connect the dots in the beginning because I was so focused on her Parkinson’s disease.

Mom was always so sharp and it was hard for me to accept that she was developing dementia along with her Parkinson’s disease. It took me awhile to realize that she was struggling with sorting things out in her mind.

Sometimes, I will just answer with a question. That way, I don’t close the loop, which just begins a new round, starting with her original question.

Sometimes, it works!

As the disease progresses it affects the parts of the brain that can create and store memories and information. Then the disease starts affecting the memory storage areas-she will lose many of her memories, working backwards in time as the disease progresses. So she has forgotten her mother died or that she was there.

She can't 'make' a memory of anything at this point, and can't retain information for more than a moment or so. If you think it's making her sad to hear about her parent's death or confusing her, it would be a kindness to avoid the topic.
This is an excellent read about the disease (at the bottom of the linked page)-it will help...
https://www.smashwords.com/extreader/read/210580/2/understanding-the-dementia-experience/Medium,Arial,Black,White,One-and-a-Half

Maybe try “I don’t know, Mom.” Then quick change of subject.

She is 88 and has dementia. This is a symptom of dementia.

Nothing “works”.

My step-mother does that, in 10 minutes she asked me if it was her birthday, 5 times, along with what the date was, I tell the date and she says oh it's 5 days after my birthday.

This was April her birth month is July,

Round n round we go, I just answer the same way over and over again, eventually she forgets about the question and moves onto another loop question.

There is no right answer, I have not found anything that will stop the process.