Pilots have been safely handpropping airplanes for many decades. Proper training and initial supervision is important, however. I've never seen anyone break their arm properly handpropping.
Certainly don't attempt it based on instruction received over the internet, however. The throttle must be set properly, and the aircraft should be chocked and tied down...at leat the tail should be tied down.
As a student, however, you really don't need to go fly when you have a system down, such as a generator failure. Or dead starter. Or dead battery. If you have a nearly dead battery, for example, you could handstart it, but depending on what type of battery you have, the high recharge that may take place when a generator kicks online could cause a fire, or worse. I've seen the terminals melted off lead acid batteries from this (and the battery cases warped), and thermal runaways in nicad batteries that melted into or through the aircraft structure.
A dead starter may or may not be a bad starter. You could have a bad relay, stuck bendix, or other problems. If the bendix drive is stuck and engaged, you might be able to handprop the engine and get it running, but with excess drag, and a chance of burning up the starter, literally. Or suffering other mechanical damage. The generator or alternator might not be outputting, or you might have another problem. I have seen belts break, brushes break, failed commutators, wiring failures, even mounting bolts break where the generator was hanging by it's shaft. In some cases, a generator failure can lead to an uncontrollable engine fire, especially a generator bearing failure (or constant speed drive failure in high performance generator systems) in a magnesium framed generator. The point is, what seems like a trivial thing may not be...don't assume it is, and knowing you have a mechanical problem, don't go flying with it. Get it fixed.
As for begging for rides...as a kid I was the proverbial airport kid. I sat on the fence, begged rides. I used to follow people to their airplane, literally, asking if they had an empty seat. I was fourteen or fifteen, and enough of a pest that the local flight school/FBO owner pulled me aside and told me I was hurting business by harassing customers. I was told to stop, and that if I would stop, I could have a job washing and waxing airplanes to pay for some flight time of my own.
Join Civil Air Patrol, go flying that way. Find owners and split some cost with them. Wait until your airplane is fixed and keep on training...flying too many different types of airplanes before you have the basics mastered may serve to confuse you. Get a computer flight simulator and have at that...simulators are useful when you apply actual experience to the simulator, rather than the other way around. When I was a kid, my instructor told me the best practice I could get was to sit in the airplane on the ramp with my eyes closed and practice flying in my mind, while touching the actual aircraft controls. If I couldn't sit in the airplane, then sit in a rocking chair with a tennis ball and a broom stick to simulate controls...but close your eyes and imagine a flight lesson, and rehearse it mentally. It does make a difference. (It's been more than a few years, but I can still remember the lessons and see what I saw then by closing my eyes and taking that flight all over again).
Fly where ever you can. Don't make yourself a pest. Experience everything you can. Your airplane will be up and running soon enough.
