(1) You’ll need to complete the Pathfinder 1 achievement, which means getting the loremaster achievement for each zone. You can split that between characters, but the Horde side requires the “Zandalar Forever” scenario, which you only get access to after doing the main storylines for all three zones. I don’t think this is the case Alliance-side, as wowhead shows only the 3 zone loremaster achievements.
You’ll also need to get the original 6 factions to revered, which will require lots of world quests in the appropriate zones.
You can buy contracts on the AH that will give you and extra 10 rep per world quest done for the faction the contract is for. It adds up over time as you do world quests. It’s a consumable that gives you a buff for 7 days. I’d probably start with the 7th Legion, as that rep gates the War Campaign (and it’s generally fairly cheap.)
(2) As soon as you hit 120, unlock world quests. (As you’ve already done the unlock on your Warlock, it’s just a quest you turn right back it. ) Then, do the Naz’jatar intro as it rewards a decent weapon early on. Follow through until you get to the quests to upgrade your Heart of Azeroth, as that will boost it to 35, and give it a hefty ilvl boost.
After that, clear out any Emissary quests that are up for the rep (and maybe useful rewards.)
For Naz’jatar:
Make sure that you do the 3 dailies for a follower each day on on Naz’jatar. (The quests themselves don’t give rep, but you get 250 rep each time they level, which takes 3 quests.) At level 5, they’ll give you a short quest that will give you a 400 rep token, so from a rep perspective, it’s good to get each follower to 5 before focusing on one. The requisition and bounty dailies only give 50 rep each, and can take a while to get done, so I’d put them as a low priority. Do world quests as you have time. (75 rep each.)
For Mechagon: Try to do the world quest (there’s only one aside from the pet battle one) but it’s worth 850 rep to complete. Then do daily quests as you have time. Keep in mind that not all show up on the world map, and some are off in hidden reaches of the zone. If you’re planning to clear out Mechagon on a given day, it can be helpful to google “Mechagon [current date]” as a couple of the fan sites have been posting “Today in Mechagon” stuff.
(3)
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Doing any world quests on the enemy continent will give 75 rep each.
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I already mentioned contracts for a bit of extra rep when doing non-7th Legion world quests.
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Doing enough Island Expeditions to fill up the Azerite bar gives a solid chunk of rep (I think 1500) and can be done weekly.
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When one of the Warfronts is in the “contribution” cycle for your faction, there will be some daily quests up for supplies that offer decent rep. These can vary dramatically in how expensive the materials they want are. You’ll get 7th Legion fast enough anyhow, so I’d just focus on ones with easy cheap mats.
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Incursions give 1000 rep when they are on the enemy continent and 500 rep in a friendly zone (they also give 500 rep for the faction the zone belongs to.) Here’s a site where you can check the schedule for upcoming incursions:
https://wow.gameinfo.io/bfa-invasions