You DO know that freezing cooked meat is quite different than raw meat, right? (also, if it’s already been flash frozen, that minimizes the amount of damage the freezing process does to the meat).
When you cook meat, it loses a lot of its natural fat content. Fattier meat tends to freeze better (that is, the quality of it seems much more similar to fresh after it’s thawed). As cooked meats are much leaner, they’ll be much different when thawed (especially the longer they remain in the freezer - due to freezer burn) - you DO minimize freezer burn by getting all of the air out of the bag and using good, thick bags though.
If the meat IS already frozen when you purchase it, I’d leave it frozen and cook them as needed. (but, I’m a bit of a purist in terms of wanting to maximize the quality of my food) :)
To answer the other questions - I’d put the frozen pre-cooked items directly into the bath and yes, you can have multiple pieces of meat in a vacuum packed bag, but they’re likely to close that gap when you cook them. (should be fine though).