A Mythic+ dungeon is a much more difficult version of the original, and loot doesn't drop directly from bosses; instead, a chest will spawn at the end containing a number of items that will increase depending on how quickly you cleared the zone. The level of this loot will increase based on the difficulty level (Keystone) of the dungeon you completed, starting at 345 and scaling to 370 for a M+10 or higher.
I've used WoW-Pro for years and in WoD, Legion and now BfA it's been awesome for just going on auto-pilot and working your way through a zone. It has 3 levels of depth you can set, so you can set it to just do 1) the main story, main points of interest and rare mobs and treasure that aren't far off the beaten path; 2) every quest with a more thorough dive into the side stuff; 3) absolutely everything.
I guess maybe I'm familiar enough with it to just slam it out. I don't recall any low droprate quests as bad as 5%. Although Blizzard has been screwing with stuff lately. Do you remember which quest it was? A lot of those can be skipped if they're too tedious. Like literally ALL the quests on that little island in the NE corner of the map with the ghost pirates underwater and the dragon whelps.
Special mention is the Darkmoon Faire Top Hat and WHEE! buff. While not always available due to the DMF being inaccessible most of the month, if you happen to be leveling when the DMF is running, it might be worth your time to go and get these. AFAIK they do stack with heirlooms, although I have not personally tested it. Fair warning: These buffs do NOT stack with each other, and the hats disappear after the DMF goes away later in the month(unless you only log in when the faire is running).