For the first request, I loved fics like The Only Safe Thing by SPowell, Communications in Binary by justthismorning, and Fear and Wanting by Barbitone, where Arthur is either socially awkward in some way or else is fearfully closeted and it takes Merlin to pull him out of his shell. I would love to find more stories like these!
The only story I have read that fits the second request would be Chrysalis by i_canz_kill_dragon. Please let me know of any others!
I'm looking for Merthur stories, but time frame (modern, canon, etc) can be whenever. Thanks!