Almost not at all... something like 50 million so far for a program whose costs are probably in the low billions. Mostly spacex is paying for it with its capital raises
Yeah, all I've heard is $53M for testing in-orbit refueling and $135M for developing the lunar lander version of Starship for the Artemis program.
SpaceX has received contracts worth over $10 billion from the DoD and NASA. Its estimated that they have over 60% of Government launch contracts.
That of course is biased towards the contracted projects, but still provides cashflow and leverage for capital.
No, government funding to hit work milestones is totally different than government bureaucracy attempting to actually do the work.