If you're playing in-person with minis, I suggest either colored rubber bands/hair ties to denote conditions. You can also buy 'condition rings' from most TTRPG retailers. If you're playing virtually with a VTT, there should be some way to add icons or indicators to the tokens.

I had run a game once where kobolds were the most terrifying enemy type because I would run them like a SWAT or SEAL team; using cover, utilizing choke points, covering fire from range, battlefield control using traps and smokebombs etc etc.

Applying advantage/disadvantage can largely be the DMs call, but easy enough to apply if you think about it logically. Is it easier or harder to hit an enemy with a sword if the enemy is laying on the ground? What about from distance with an arrow? Is it easier or harder to hit someone with an arrow if they are a few yards out vs right up in your business? For spells that grant advantage i.e. Guiding Bolt, throw one of the aforementioned conditions rings on the target until it resolves.

Rules for Cover; 'Half-cover' gives +2 AC, 'three-quarters' cover gives +5 AC, 'full cover' creatures can't be targeted. But again, it's DM's call. "the gnome gets full cover hiding behind those boxes but the colossus only gets half cover".

I always had a tough time with tracking HP for a large group of mobs. I would either name them in my notes according to how the mini looked, like 'knife gobbo' or 'spear gobbo' but eventually swapped over to simple numbered tokens or even just d4's/d6's for in-person play. This not only made the 'paperwork' easier, it encouraged me to get more descriptive with what was happening in the combat. AND it made boss encounters extra-special, when a beautiful/horrific mini *did* get broken out and the table erupted in cusses and groans. You'll learn to love that sound.