If you would like the help, I would be happy to coach you. You have a good start here, and since you are using a microprocessor there are some things you can do to enhance your system.
On Amp/Hour ratings, a 7AH battery will provide 7 amps for one hour, or 1 amp for seven hours. Unfortunately for your fuse, it will also provide 14 amps for half an hour, depending on the load.
Very detailed post, good work too!
RE: Solar power project step 3, circuit designs for charging / power out switch for continuous(ish) use, and new batteries