As a way to sort it down to different causes, there may be enough access to spot a few things to test.
For vacuum testing, finding a common point where a bunch of the lines come together may be a start. If you can spot which lines go to the levers and flaps on the heater, pulling different lines off and holding a finger over the hole on the fitting, can let you tell where you have vacuum and not.
While doing this, it may help to have a helper try different setttings on the heater. If you have a tube which has split, taking it off the system and stopping the leak with a finger, may let the rest start to work as they should.
Much depends on luck?? Can you find them and can you reach them?
For the fan speeds, it is sounding more like a defect in the electrical part of the controls, either at the control body or at a resister pack that is often mounted on the heater body where the air flows. The air is used to cool the resister coils.
If you are not familiar with these, it may be worthwhile to do a search for "resister pack" for the chassis your RV is on to get a look at a picture to ease spotting it?
This is the type I normally thing of but know little about the pusher group:
https://www.homedepot.com/p/HVAC-Blo...CunFdkzxYGzwLM
Idea is that the switch changes the route of the power to the blower, making it run through different levels of resistance to get to the motor. That changes the speed of the fan, but if one of those routes through different coils goes open or changes, the fan speeds will not all work!
The route going bad CAN happen in the controls or at the pack but it is semi-common at the pack. Simple wire springs that heat and cool to eventually break kind of like a filiment in light bulbs ?
Where do they put it on the pusher group? On front end gas, it is often just hung right on the big plastic "cover" which carries the air over the heater,etc and to the different vents. One big central point where all the vents come together and spotted by the wires going to the pack, it is often only mounted with a couple screws.