I only got part way though the expansion when it came out, I decided to try the new DH spec and went to Shadowlands. I went through all the 4 lands and choose my covenant. Do I have to level my renown and fill up the anima thing before I can do the Maw stuff?
You should have access to the Maw starting with the second chapter of your covenant campaign. I believe you get Korthia access after chapter 3. Chapter 2 of Korthia/Chains of domination should give you access to mounts in the maw, and chapter 3 should remove Eye of the Jailer.
yes but only if you havent done it before .. I was able to skip to the maw , korthia and into zereth mortis after doing the early covenant stuff(till the told me to go back to oribos)
You can buy a 60 renown token at the vendor beside the flightmaster in Oribos.
you dont have to level it up, but you do probably have to do the introductory quests that introduce you to the anima collector and the soulbind interface, but that should only take about 5 minutes.
also if you care about story, dont choose the “i’ve heard this tale before” options. those are skips that will autocomplete scenarios for fast unlocking of the later zones. if all you want to do is farm cosmetics and achievements then those are fine, but if you want to play through the actual story dont click them
and if you’re worried about the renown grind with the covenants, just be aware that each raid boss on each difficulty will drop a renown token. you can get 40 renown a week on castle nathria alone if you complete all the difficulties
OP, you don’t have to if you don’t want to, but I highly recommend you get the addons BTWquests and BTWquests Shadowlands (as well as for all other expansions you want to level in - you don’t have to have them all enabled at the same time - just BTWquests and the BTWquests of whatever expansion you want to be guided in).
It tells you exactly where to go for quests and quest NPCs and where to unlock any area, zone, any expansion or even any part of any expansion (like the Maw, convenants, campaigns, Ardenweald, Revendreth etc). if you want to do what and what prerequisites (what you have to do first) if you want to unlock any other part of the expansion.
This goes for all other expansion BTWquest addons. It’s up to you, of course, but these addons have been an in-game life-saver for me personally.
All the best and happy levelling. 
