After restart, Mail and iCloud don't work

Everytime, after I restart my iMac, I have problems with Mail and iCloud. First, it keeps asking for my iCloud password (the same as my Apple ID password). No matter what I enter, it's not accepted. In the end, I have to reset/change it (already three times so far this year).

Then, my gmail and iCloud mail accounts don't work in Mail. Stuck with the little squiggle sign. No matter what I do, nothing works. I just wasted another hour poking around with this. I try the Window>Connection Doctor. Again, no luck.

When it asks for an email password, I enter it carefully, then get a new small blank window with heading asking for the password (which I've already entered) but there's no place on this new window to enter it -- the body area is totally blank -- and the only button at the bottom is "Cancel".

Meanwhile, my Mail activity window is showing something like "350 new messages" (which is absurd) and nothing happening.

WHY is this happening? And HOW can I get past this? It is so-o-o-o time wasting!!!!!