How much repair should you do on a keep/castle before leaving them for the next objective?
Up to you but best to repair walls to 100%. If you are trying to earn AP to level up your Assault line, etc, and have difficulty killing other players, then one option is to go around to all the keeps and resource towers etc, and repair everything.


Do guilds pay attention, or are support activities pointless anyway? I've seen a lot of castle being taken, and as soon as the flag flips, most of the group run off to the next objective, leaving wide open gaps in walls and collapsed doors.
Usually they do, but sometimes people don't have any repair kits left.

Is there a time limit on capturing as many keeps as possible for the points?
I think the time limit has more to do with preventing factions from exploiting by flipping objectives frequently. Something in the range of 5 minutes I believe.

What purpose is served by controlling lumber, mines, farms?
Farms increase health of the NPCs, lumber increases strength of doors, mines increase strength of walls. In addition, when all these are increasing in level, the NPCs get some special attacks. (You can see the level of the resource by clicking on the map)

Do these resources help the nearby castle or hinder it if owned by the enemy?
Yes, they remove those buffs from NPCs, doors, walls etc.

What exactly happens if I pick up an Elder scroll? What commands still work. Where am I supposed to go?
You can't hide or stealth while holding. You are supposed to go to a keep where you want to deposit the scroll. If your faction does not hold your own scrolls, then you won't be able to put down the enemy scroll until you first retrieve your own scrolls.


Is there any benefit to staying in the field versus running for a castle?
Instead of immediately returning, some people use the scroll as a way to attract enemy players and kill them for alliance points.

How much different are the activities in the various campaigns? Are some more focused on fast raids and others on long-term occupation?
The activities are the same. On NA PC however, we have only one campaign with decent population (Vivec). The others are low population. Sometimes Sotha Sil (non CP) or Kyne (below 50) have good population around prime time, but the others don't have too much going on.

What can I do with Alliance Points? I've been spending mine on siege engines and repair kits, but considering the lack of repair, there must be more things to spend them on.
Personally, I try to save my alliance points to buy bind on pickup monster helms. Every weekend there is a vendor at your faction base who sells gold jewelry and monster helms. Also you can use alliance points to buy items like militant ordinator motifs, akaviri motifs, many different set item containers available in the towns.

Any pointers on using siege engines, like you can fire 3 ballistas for more damage in the same time you can fire a catapult or don't aim for the door - aim for the walls?
Well just keep in mind the stone items are better for walls and doors, and fire items are for killing players.