It's more on BRD on what is expected of me. Since I haven't played WAR or WHM I only do Mage's Ballad when I see the WHM MP about half.
This is always tricky because it depends on if your healers are good or not. Unless there is a ton of AoE damage going out or raises I usually don't do it unless they are low and ask for it. My experience playing sch and whm is that when bards throw up ballad I rarely actually needed it between aetherflow/energy drain/shroud of saints/ethers. If the healers are burning mp overhealing or not using those properly you might need to ballad though, in the end that's something for them to correct though.
So with that, am I suppose to throw up Mages and Army right away?
Never right away no.
Paeon you will need to use even less since tp needs are usually taken care of by having to step off the mob to deal with various mechanics or just pauses in combat such as when garuda jumps. If people are popping invigorate as soon as they are down to 600/500 tp they shouldn't need Paeon unless the fight is going for 4 or 5+min of constantly riding the GCD, or if people are reapplying their dots too soon since that starts to burn TP fast. If a lot of AoE damage needs to go out and you don't have blms the melee might need it since physical AoEs are really taxing on tp
You can usually open a fight with Foes Requium with it going off as the tank pulls so it's up for magic dots although there are some where you might want to wait till after the initial phase. Then when you have mp back ride Requium some more unless unless your healers are burning mp or it's a fight where paeon is a thing. You can also pop battle voice with the first requium unless you know you will need it sometime before 5min into the fight.
I have my rotations for solo mobs and sack pulls down pretty good. But even now, I am still learning that Blood for Blood and Raging Stikes stack for a 40% damage dealt, or has that been nerfed?
Blood for Blood is only 10% as bard so 30%, unless you need to put your damage in a specific spot in the fight you generally want to try to use your cool downs as much as possible so you can use them more.
It's hard to give just general advice for bard because you often need to work your cool downs around specific mechanics/phases and song usage can vary by people in your party XD