Good diagnostic post! You have a number of safety issues, chief of which is all those receptacles and 12/14awg wiring should not be fed by a 30A circuit breaker. How fast you decide to fix them is up to you, but you're right that it is a fire hazard.
For example, a 14awg NM-B cable can carry 15A without exceeding a 60C design temperature (someone will surly correct me if I'm remembering the values wrong.) The requirements for installing this type of cable (no conduit needed, okay to be in contact with insulation, etc.) are specified with that 15A in mind. When you exceed it by using a 30A breaker, some person could plug two big space heaters into a receptacle, cause the 14awg cable to overheat, and it could start a fire, all without tripping the circuit breaker.
My suggestion is to start by replacing the 30A breaker. If you change it to 15A the wiring you have currently (aside from the improper splices) is basically safe. If you change to a 20A breaker you will need to upgrade the 14awg wire to 12awg.
Book recommendation
By the way, you may want a book to help you get started. As @ThreePhase explains, there are plenty of other things you want to do to make all this safe and up to code; and it's hard to cover them all in Q&A form. I like the Black & Decker Complete Guide to Wiring, which is available at home improvement stores and many libraries. It's heavily-illustrated and aimed right at DIY homeowners.