Beware of the cashier's check in the mail! That is most certainly a scam. Do not even attempt to deposit or cash it as it will bounce. Legitimate companies do not send you money BEFORE you have performed shops. Scams want you to cash the bogus check and wire transfer money to them. When the check bounces you will discover you wired away your own money as you will need to make good on the money received from the bogus check.
Read through this section of the forum, starting with the Nuts and Bolts thread, for an idea of how the real mystery shopping works.
In real mystery shopping you generally make small purchases, for which you will be reimbursed if the shop is accepted, in order to get a receipt to prove you were at the right place at the right time. The items are yours to keep. There are some shops for which you are not reimbursed for your purchase because as part of the shop you are to return the item. There are shops that require larger cash outlays, such as restaurant shops, where there may be little or no fee, only reimbursement.