Temple Medallions delete when I click them?

Whenever Alva gets a medallion what determines when I can click on it to use it? For example, I just did a run where I got TWO +6 crystal medallions. I finished temple, went back to the start to close it and:

1) Only one was in my inventory when I had room for two, these cannot stack? If not can I use that right when it drops, while in temple run?

2) When I was closing temple I saw the +6 and clicked it, never got 6 more and it just went away. This is such a bad design, at no point in time was I made aware that I'm in a "delete" mode.

When can I use these?

I have the opposite issue. I only drop medallions from architect. I have some T3 rooms and none of them show they can drop medallions. Do I need to have +6 medallion capacity before they start dropping?