Those 2 wire devices are 12v dc. (Make sure they are though)
You can get cheap rocker/toggle switches for them or hook them up to a relay.
Yes you will want to fuse EVERYTHING connected to the battery. You can get fuse holders or make your own pretty easily.
Yes you can probably tap off of the power inverter inputs as a fan and led lights will likely not draw much amperage at all and won’t effect the inverter. However, you still want to put a fuse between the fan/LED lights and the inverter 12v inputs. Check the amperage draw on the led’s and the fan. Or do what I do - try a small fuse first, then go the next size up if it blows under normal usage. This allows the best protection in case of any problems. One main issue with fuses people have are the fuse holders of fuses melting - not from overdraw but because of poor connections. Make sure you use the correct size connectors for everything.