Beginner Body work

Again just my $.02. With the rust spots I would sand and spray with self-etching primer and just get a rattle can of paint that matches your current color as close as possible. Your car may be spotted for awhile but it would stop the rust. Try not to think of painting the whole car right now. If you are planning on painting the car your self this would buy you time to get tools needed. You would also be learning on the small spots to help for the WHOLE JOB.
If you do take the car to a shop to fix the leak just ask them not to use body filler to fix the entire thing. Some shops would just fill with filler and paint over that. Ask them to patch in the work for a more permanate fix. it will cost more but will save more later in the project.
Working on the car without a garage is done all the time. you can do it but it is not the prefered method. I done most of my truck in the yard and then borrowed a friends garage to do the final work and paint. I know here in KY you could buy a porta-car-port ( metal frame with roof) and just use plastic on the sides for a paint booth. They cost $699 installed.
Good luck on your project.
Jeff