Hi laur371!
I have a few answers that I hope can help, but I would first say that because Coyle does things a bit differently than many MSPs, the answers in this thread should be viewed as regarding Coyle and may not apply to MSPs in general. On to your questions.
1) Each listing is for one shop. Personally, I have seen Coyle list one client with multiple shops in a month, some with different meal periods. So, what you see is what you get on the Coyle job board. In the mystery shopping business, restaurants are often shopped once per month. But it varies with clients. Some are shopped once a week, twice a month, or less often than each month.
2) You have found the dreaded "black hole" of an application in waiting. It's not fun waiting, especially if the answer is holding you up with planning your schedule. The answer depends on the scheduler, some work Monday to Friday 9-5 or on an irregular schedule, how attractive your application is, how close the deadline is, how likely an application from a more seasoned shopper might come in, and perhaps other factors. You might send an inquiry to the scheduler after a few days or more, depending on the shopping period. Some of us will end our applications with a deadline to respond, saying something like, "This application expires on -fill-in-date-here." The good news is the waiting becomes shorter as you develop a track record of being dependable and following instructions.
3) I would be truthful and explain anything that seems unusual. If you want to put every day of the month, explain why. Although I think it would be more believable to be much more limited in availability dates.
4) For Coyle, I have found them willing to read detailed requests. For example, one month I wanted to do one shop for them and had two Saturdays available. I applied for three restaurants (I didn't care which one) with that request and they gave me one shop on one of the requested dates. For you, I suggest you start with your preferred times saying exactly that and also say you are available at other times. Also, they do request an update with any changed availabilities. If you change or refine your availabilities, that might be a way to "remind" them of your application.

As for being flexible enough, I really don't have much insight as I haven't given many dates and have been awarded shops. What else can you do? See the next paragraph.
5) Yes, they do have a shopmetrics site as well. It is optional to sign up for the shopmetrics site. However, signing up there and other MSPs can be helpful, at least down the road. Schedulers care most about reliability and turning in good reports when they choose from different shoppers. With no track record at Coyle and little if any as a mystery shopper you can use the Coyle shopmetrics site to possibly get shops that will show them you are that for future restaurant applications. You might also do restaurant or even hotel shops with other MSPs.
Happily shopping Rhode Island and nearby Massachusetts and Connecticut