I think the person whose input you need most is your moms and that you should discuss these questions with her. If you don't have the kind of mom where you can discuss these issues with her (and certainly that is possible), I think a situation where she is providing you with regular childcare may prove nerve-wracking for everyone involved.
Here are my answers to your questions when I was similarly situated --
1. How much pumped milk do you bring for your child?
Despite extensive pumping (and nursing) I never did produce enough milk, so used formula (powdered) as well (i.e. I breastfed, but not exclusively). Obviously it was easier to have the formula used by other care providers, so that's what I did. Unless you are hoping to avoid formula altogether, I'd recommend having a can, even if just a small can, handy when you first leave your baby with your mom, that way if she ever runs short of milk (if you didn't bring enough), she's got an alternative.
2. Did you provide all of the extras i.e. highchair, cups, bowls, spoons?
I don't think so, but this seems like a question best directed to your mom -- what would she like to provide and what do you need to bring? What would she like you to purchase so she has them handy?
3. Did you pay your family member anything for helping out?
No, but once a week my mom and I (and my son) met for breakfast at a local food co-op, my treat. Then she took DS and I went to work. Provided a nice chance to catch up and to communicate about plans for the week ahead.
4. What is your cloth diaper routine? Did you simply bring home the dirty diapers daily or have them rinse at their house?
My mom kept her own set (provided by me) and washed them at her home, way easier than hauling them back and forth and she was unflustered by this being part of the routine. Yours may feel differently. Her also having several changes of clothes for your baby that just stay at her house is probably a good idea, there are always "those days." My mom still keeps a couple of changes of clothes for my son, and he's now an elementary schooler. The cause of problems has changed (now it's muddy soccer fields, then it was spit up and poop), but the problems persist.
5. How often do you have to pump while at the office?
I typically pumped 3 times/day at work (mid-morning, lunch, mid-afternoon), but -- see above. No idea if what I did was typical.