To run 110/120 volt items you need a inverter and need to check a amp chart for running those items. Most modern inverters have alerts
when the battery reaches a low level allowing you enough amperage to start the car and charge the battery(s).
Run proper wiring with a inverter. I can not stress that enough do not go cheap on the wire for the amperage the inverter is capable of. And run a fuse from the battery to the inverter. You can easily install a weatherproof ANL fuse/holder at the battery terminal then run the wiring off of that. In the event the cable comes loose from the inverter or gets severed the fuse blows to keep you from having a live heavy gauge wire from grounding out.
If you google the thing you are wanting to run you can generally find what it needs in watts then mount it in a manner so it will not become vibrated to death. The vibrations are what will kill items meant to sit in one spot in your house more then the temperature swings or varying amperage that a car experiences.
Also remember that power required = volts x amps. When you want to generate 120 volts from a 12 volt system, you cannot expect to get the same A/C amperage you get at home.
Household receptacles can provide 15 amps, but most inexpensive 12 volt inverters only provide about 5-10 amps of A/C power. If they draw more than about 10 amps from the car's 12 volt system, they also need to be direct wired because typical cigarette lighter plugs are rated for 10 amps.