Hello - good questions as you're getting started. I recommend that you read Flash's sticky: [
www.mysteryshopforum.com]. It will address many of your questions.
I don't have an EIN and, unless there are extenuating circumstances, it is neither necessary nor advisable for a mystery shopper to get an EIN.
MSPs may issue 1099s with an amount including both reimbursements and fees; however, it should be fees only, as only fees are taxable. Keep track yourself and address any reimbursement amount on Schedule C by subtracting reimbursement dollars. Again, read the Sticky, and also you can find discussion of this and related matters by using the Search feature.