First, welcome to the forum!
Yes, most of us know an EAD as a "work permit" which allows you to work in the country. Your TIN will indeed allow you to register with Mystery Shopping companies so you are good there.
SASSIE is a reporting platform that many Mystery Shopping companies use rather than develop their own software. You can think of it as an application or program such as Facebook or other piece of software used but not owned by the user. There are similar platforms with Prophet4, ShopMetrics and others. Then there are companies that use proprietary software which they create and maintain themselves, such as Market Force, Sinclair, A Closer Look and Maritz.
As far as security is concerned, anything on the internet is subject to being hacked. A hack can occur at the user level or the corporate level. I got notice a few months ago that my information had been hacked because I was used as a reference for a person applying for a job with the US Government. I have had my personal information compromise by a hack through Target. Most recently my personal information may have been compromised when the lab that does my medical bloodwork was disposing of old records and a container on the back of the truck taking records to be shredded opened and medical records were blown out all over the neighborhood. In Mystery Shopping, companies I have been registered with have been hacked, outside schedulers have downloaded databases and companies have closed, having their computers seized and sold at a Sheriff's auction to cover unpaid rent. Overall I am convinced that my TIN can not be guaranteed safe by anyone at any time. It makes sense to be wary and try to protect it, but you just can't. If you rent or buy a place to live you need to give out the number. If you have a bank account or credit card you need to give out the number. If you have a job or insurance or a car or go to the dentist or doctor, you need to give out the number. With many companies you cannot be accepted as a shopper without a TIN, so you just do it.
This forum will give you a good notion of what companies are good to work with and pay when and as they indicate they will. There are 3 major ways that companies pay--by check, by direct deposit to your bank account and by PayPal. Many companies will only pay by one of these methods and most frequently that is by PayPal, so if you do not have a PayPal account, I would suggest you open one at PayPal.com. You can get a free account. You also need to have an email address for mystery shopping that should be an address that links to your PayPal account to accept payments. I would strongly suggest you open a separate email account with Gmail just for mystery shopping.
At the bottom of each page of the forum you will find a link to our "Official List of Mystery Shopping Companies". This will provide you with links to conversations about the company as well as links to register with the company.