Is the ilvl of dropped items determined by map level or mob level?

Mob level. So take the ilvl of the zone. Normal mobs drop that ilvl, rare drop +1(or 2 seeing some conflicting answers), and unique drop +2. Ways tones only drop the same tier of ways tone you ran. You need to fight a powerful boss with lets say t5 to fet a t6. You can also just reformed 3 t5 ways tones into t6. As well as doriyani selling the highest tier of map you've done -1 in his shop every level up. So you can go to Doriyani, buy 9 t4s and reformed to a single t6 if you wanted to just jump. That's how ppl speed run t1-t15 really fast.

kinda, monster level does decide the ilvl of items you get, but there's an easier way to get the next tier of tabs. You can put any 3 n-tier tablets in the reforging bench and get back one n+1 level tablet. (throw 3 t6 tabs in the bench and you will get a t7).

You need to clear the corrupted zone bosses at increasing levels to unlock higher tier of waystones. Enemy level and waystone level with result in better drops, tho omen of light and perfect essences can drop at around tier 8 so other stuff can too.

Mob level, but that is determined by map level. There are i84 mobs (t17) in i83 zones, IIRC rarity of the mobs (white blue yellow unique) effects the +mob level in the zone

It does increase drop level.