AMR asks me to equip really weird/low ilvl items for my tank! Why?
This should be fixed now.
AMR tells me to equip this lower ilvl item when I know I have the same one but higher ilvl, why?
This is most likely because you have priorities for your specs, and currently looking at a spec with lower priority where a higher prioritized spec have already taken the higher ilvl item. AMR will not take an item from a higher prioritized spec if it requires to re-enchant/re-gem/re-set azerite powers. AMR is trying to be kind to your gold! 
You can re-order your priorities on the left hand side of Best in Bags.
I want to be able to set priority like #1 DPS (Single), #2 DPS (Multi), #3 Healing (Raid), etc…
This is in the works, stay tuned!
For healing stats, it seems AMR is prioritizing Versatility a lot higher then any other site. Why is that?
I still have problem! Please help!
For AMR to help out as quickly as possible, please share your addon string you get from in-game! That way people here on the forums can paste it into the website and more quickly take a look and try to help.