Hey Ken!
The module will hit a few of these use cases. Not quite sure how having someone else pay the deposit/full for them would work. Might be another module or maybe just a set of attributes?
Fixed deposit amount is already in the module. Multiple partial payments can be made based on an amount you set (maybe can be switched to be user configurable?). I think out of the box this will take you pretty close to what you're looking for.
We just need $300 more via ChipIn and we can get this thing release and a few of these new feature requests in place!