As someone who has completed legendary for both sides, let me give you some pointers on your points.
On maps where you have to take objectives, rushing for them is more or less the only way to get it done. Find weak spots and go for them. On CSA side Shiloh phase 1 i went with a rush for the left side, then along the "ridge" behind the farmhouse. Pretty much pushing them towards the middle of what become the big map. For phase 2, the opposite, rush down to the right, cross down by the swamps and hold the forrested area at the top of the map, beware tho, reinforcements can spawn ontop of you if you missplay. After that, just push along the edges and take the landing before things get to ugly.
Get the fayettes as soon as possible and equip a brigade with them. Have them in the battles, but don't actually use them unless you really really have to. This inflates the AIs weapons and you get better weapons in the captured pile.
This is very true. But you should still stay as long as it's still "profitable". If you have perfect cover ( and i mean 100% cover with flat terrain infront ). Don't capture the objective if you don't have to. ( edit: you should still rush to a position where you can take it with minimal casualties ) Just sit there and collect monies. Yes, think of kills as money, it helps.
Don't use skirmishers and don't use cav. With the extra manpower added to the AI, any brigade of skirm or cav you have in your army will turn into deathmachines spawned by the AI. So it's actually better not to use them at all. Okey, maybe if you have some extra cash laying around you can grab a cav or 2. But the consequences might be horrible. ( When i played the CSA legendary i tried adding a 300man cav unit for the mission Ambush Convoy. This gave the AI 6 units of 500+man melee cav. Happy days! )
I've tried this out alot of times and have found that it's more about positioning. But i might be wrong on this one. What i have seen tho is that if i don't leave an opening, i don't get rushed.