If the hose comes out from under the pressure cap but above the rubber seal in the cap thats just a vent that dumps to the outside world when the radiator cap releases pressure.
Your starter sounds like a bad starter gear bendix ratchet widget. Its supposed to turn one way but not both in case the engine startes and the starter is still engaged, yours is turning both ways. Time for R&R. A trick I can't explain is to let go of the starter before it disengages. For some reason the engine will start when you do that, even though its cranking less.