It always makes sense for folks to be objective about any communications they receive unsolicited that may involve their time, money or other items of value. Probably the most useful phrase to remember is "Too good to be true." This applies to any confidence game, whether it is that you purportedly have won a lottery you never entered, have had an unknown relative die and leave you tons of money you need to pay some legal fees to have released to you, are being offered too much money by strangers to do mystery shops or other errands.
You protect your identity by not answering pfishing emails that are requesting passwords--legitimate companies tell you to log on at their site to deal with any issues and don't provide you a link to do so. If you don't know how to get to the site on your own then it is probably not worth your time to go and clarify anything anyway.
You don't send your personal information to strangers by email over the internet unless you are 100% certain they are who they purport to be and there is no other way. Certainly in mystery shopping the first step is to register on the website of a legitimate company and most legitimate companies offer a secured website to do so.
If you receive checks in the mail you do not know who they are really from and what they are really for, don't cash them. Mystery shopping pays AFTER the work is done and accepted, so checks received in advance are going to be scams.
Con jobs and other scams appeal to our avaricious natures and our sense of need. Don't be a victim.