In my Imperial campaign i only use two kind of offensive fleets. One is a standard Imperial Navy fleet fielding 3 Retribution class battleships. The other is a Adeptus Mechanicus fleet fielding 3 Ark Mechanicus. I never use boarding actions so i can keep my troop numbers and only rely on my guns and abilities to beat the enemy. The best way for me is to deploy the Mechanicus fleet first and use all my nova cannon charges on the enemy before they come into range, at least one leader should have the Augur Probe skill or if you like put in some escort ships, im just sick of replacing them all the time and its not needed. Next step for all enemies except the Orks or Tyranids is to charge straight into the enemy battle lines, preferably splitting the enemy force so my ships can fire from both sides as much as possible. Warp out ships when they go below 50% health and get Retributions as reinforcement. If facing the Orks or Tyranids do the same but run the fuck away as soon as they come close and keep at range trying to circle them while firing the guns and using all abilities available to kill the first wave as fast as possible, after that its quite easy to take out the reinforcements as they enter the battle one by one.
But this is single player, i dont play multiplayer (yet) but it makes perfect sense that tactics should be favored over size and in my opinion thats a good thing. The main advantage of big ships is the amount of damage they can take and as such i would think the primary purpose is tanking damage while the rest of the fleets sets up an ambush. Of course i cant comment on how applicable this is because i havent done any multiplayer yet but i would guess it doesnt work too well since even a battleship will go down fast if it faces the whole of the opposing fleet, especially if they are smaller more nimble ships who can circle around it and get to the weak rear. Another good thing about the big ships is the ramming but i suspect this will not matter in multiplayer since real people are not as stupid as the AI who death stacks all their ships into a neat row that is just asking for it.
In my opinion the mobility of the battleships needs to stay the same, this is supposed to be the main weakness of a big ship, trading more guns and more health/shields for reduced speed/turning. There is some things to consider though. Maybe granting the battleships the fast turn of the other ships in the fleet. Or possibly giving battleships the micro-warp jump ability as a default since as others have said if you get surrounded you are pretty much out of luck, but if you could reset this with a micro-warp jump you would regain the advantage for some time.
Other possible improvements could be increasing the damage of the guns, but this would make battleships ridiculous in the campaign where they already face-roll everything.
Another thing could be increasing hit points and armor but this would have the same effect of making them really overpowered in the campaign.
Maybe the shields could be increased and the regeneration buffed because this plays a smaller role then the overall hit points but i suspect this would also make them overpowered in campaign.
A good solution could be reworking the boarding mechanics of progressively bigger ships, a bigger ship should have more assault craft and a bigger teleportarium either delivering more troops in one blow or being able to deliver troops more frequently and with a higher max usage number. The overall number of troops should be increased too since a Space Marine fleet can instantly take out an enemy battleship with all boarding actions used and thats a pretty big hit to a fleet losing the most powerful ship in an instant. However since the boarding mechanics are being reworked maybe that will fix some of these problems giving the battleships more staying power to deliver more damage. It makes perfect sense lore wise but you cannot balance Space Marines of lore since that would mean they would dominate everything and everyone.
The other abilities are already handled pretty well as battleships have more turrets and a stack of 3 battleships can shoot down every torpedo coming at them 8/10 times and also handle enemy fighters/bombers pretty well.
Problem 1. What are you talking about? Im pretty far into the imperial campaign and if anything there is way too MUCH resource gain. There was some resource managing the first like 20 turns maybe but after that i dont even have to consider what resources i use or lose. I play on normal difficulty but i cannot imagine there is that much of a difference, i have over 10000 resource and i cannot spend it faster than i gain it. If i wanted to i could sacrifice space stations, turrets, ships all day long and just replace them, except the shipyards wont generate points fast enough to replace ships. The resources however is not a problem, it increases exponentially. Just upgrade and capture all resource gaining planets first and soon you wont have to worry at all.
Problem 5. Generally it seems that the participating ships of secondary fleets if possible will be the flagship followed by the strongest ships available and almost always you will get the escort ships because they are low leadership and fill up the last bit available. Personally i dont really see the use of deploying weaker ships, for me the BS is where its all at. Running only BS in my imperial navys against the AI, they can deploy all the cruisers and frigates they want but they wont beat the hull points and damage output of my Retribution and Ark Mechanicus lineup.
Problem 6. I do not have this problem. First of all you need to be sure that the enemy flagship actually has battle plans, which you can see by the battleplan icon next to the ship health/shields. If they do have battle plans board them and you will get them, they might steal them back in which case you will have to get them again with a new boarding operation.