How long should I stay in Anemos for just doing challenge logs/fates each week? What's the best level to move onto Pagos?
At least 25. You can't begin gathering light in Pagos until then and getting around the map is so bothersome that it's not worth it before then. You might even push it off until 30 so you can grab the Geothermal Studies aetheryte which will give you access to the northern half of the map considerably easier than walking and 90% of the FATEs that the train will spawn.
When I go to Pagos - what's the best course of action? Getting around solo seems kind of difficult.
Follow the train but probably stick to the southern half of the map until you get the Geothermal Studies aetheryte or a two-person mounted teammate to ferry you through the long, dangerous corridor between the two halves of the map.
What's the most efficient way of farming light now? Do I just hope to find a party in there?
Kill dragons on their own or the one at the entrance to the Crystal Forge. Killing the dragons on chain kills 5/10/15/20/25/30 will award a lot of light if it procs. Do FATEs when they spawn, they give guaranteed light too.
Just shout for a light party. There are plenty of people doing it.