You can usually do multiple shops of the same sort. However, it is common for a client to have limits on the number you can do in a given time frame. Such limits are usually written in the shop guidelines. If you want to do, say, a dozen shops at different Costco stores, apply. The worst that can happen is that you are told "no." Of course, only apply if you are ready to do all of them.
Yes, that's right.
In the specific example of Costco shops, a lot of shoppers do several shops (price audits) at the same location simultaneously, and then they do the same on another Costco location, often on the same day.
I remember there was one person who completed a total of 30 Costco shops in a single day - 6 shops per location, 5 locations in total. However, this is not so common, and you have to be fairly experienced in those shops and comfortable with doing multiple shops in one visit, as well as familliar with the locations layouts, as each shop requires you to spend more time at the location, risking to be discovered as a shopper.
For starters, you can try doing 2 (or 3) at the same location in one visit, and/or doing shops at various locations. It's certainly doesn't hurt to try, and take baby steps until you're comfortable with doing as many as you'd like.