When are they going to recalculate the Tithe, and can we voluntarily pay more than our amount of the Tithe?
You can pay more but that just means they ratchet up the cost next turn. The Tithe is meant to be 90%-100% of your Extraction in Resources/Manpower per turn. No one actually pays that much because no one is dumb enough to overpay which means that the Administratum is stuck with only the more reasonable average of 10% of your Extraction as Resource or Manpower based tithe.
Generally the Administratum will try to force planets into paying up to 50% to 75% tithes, but most
important planets lower that to 5% or so. So backwater Industrial world with an Extraction of 100 is probably paying around 75 Resources per turn while a Forge World with an Extraction of 10k is only paying 500 or so Resources per turn. In short the more important a world is the less leverage the Administratum has over it.
Paying
more is just
begging them to do an audit and determine your
actual tithe. Which would mean that your tithe would spike to ~1743 at the low end due to your current income until you could bash it back down. In short the Administratum is
lawful stupid of the highest order, it does not care about ensuring that worlds can actually do their purpose. It would
gladly drain Cadia of all resources into the Tithe if Cadia started overpaying. If they could get away with it Terra and Mars would be paying millions of Resources per turn and they would let the trillions upon trillions that would die from that die in favor of getting the money.
and then send detachments to support each and every Astartes Chapter in the system, alongside supporting battlegroups.
That will insult the Astartes massively as in -50 Favor from all of them outright. Astartes
do NOT like it when mortals start acting like they
matter against the threats that the Astartes fight. Astartes are more likely to kill your private army out right than work with them in that manner. Astartes are good with mortal support when
they arrive to a battle field, they get really insulted if they perceive it as humans acting like they
need human support.
when was the last time anyone asked the Space Marines how they could help them, huh?
They would say: Stay the hell out of our way, we have no need for you and you will just get in our path. If you care to keep your head stay far away from us while we solve the problem. If you want to be helpful go make us some more power armor.
Unironically, seconding proper task group support to literally every Chapter in the Sector will likely make their jobs a lot easier, because it's help, right there, right now, already under their command, and when the Space Marines can do their job the Mortals rest easier ya know?
Not how the Astartes would see it, they would see it as a mortal human implying crudely at that that they
require external human support to be effective.