1) Just because a company is a member of the MSPA is no guarantee of 'reputable' though it does tend to be a general indicator. It mostly means they paid their MSPA dues and gave lip service to behaving professionally. I would strongly encourage you to rather use the list at the bottom of each page of this forum as "Official List of Mystery Shopping Companies" because these are companies for which you will find discussions on this forum by shoppers who have actually worked with the companies. The companies don't buy their spot on the list here by paying dues.
I don't know about the 'just an email address/phone number' issue because I don't use the MSPA site. But it seems to me that PayPal and some other companies that offer no shops and do no scheduling have paid their MSPA dues and are or were on their lists.
2) Companies will generally not let you see their surveys before you have agreed to perform the shop because they consider these things to be confidential. Some companies will not even let you know who you are shopping until you agree to perform the shop.
Confidentiality - When a company spends the time and money putting together an evaluation tool they are hardly interested in having their competitor just steal it, make a quick change or two and use it themselves. This has happened and does continue to happen, but the companies try to prevent it. Similarly, if I am an employee at XYZ and discover that MSP ABC is the company doing shops on which we keep getting marked down, if I could see the shop dates and see what I am being evaluated on, I could get the bonuses for scoring well on the shop. Yes, it does happen. Again it is in the best interest of the integrity of the shops to prevent it.
Yes, sometimes you will find that a shop is just not worth doing. There are graceful ways of quickly cancelling out so that they have plenty of time to assign the shop to some other shopper. Many of us will go ahead and perform the shop on a one time basis to avoid cancelling and indeed it may not be nearly as bad as it looks on paper.