Your questions are difficult to answer. What I would do is take a sample of water from all different areas of the pool. The more samples, the better. Mix all together in a bucket and then test for metals. You could use the pool store for this one. Or you could use a submersible pump to grab water from one end and bring to the other end, mix for a few hours, and if possible use a brush to try mixing by hand. This requires the cover to be lifted.
FWIW, I had the mineral cartridge in for a year, not the tablets with the Frog System. No staining whatsoever in the pool. But, I do not believe anyone will provide you a concrete answer if staining will occur. You would have had to communicate this with the pool company prior to closing. I always recommend for someone to be home for the closing. Locking the gates really makes a difference if they do not listen.