Maybe. Ignition switch failures tend to cause all sorts of weird glitches and it's common in Nissans for it to fail, so I'd change it, it's a simple job and relatively cheap. But I would also look at the relays in the engine bay. Try swapping identical relays and see if some of those issues go away.
To give you an example: my AC was randomly spewing warm air. I replaced the HVAC module and it was doing the same thing. I even disconnected the air mixing actuator. In the end the problem was the relay that controls the AC compressor which was intermittently failing and I found it by swapping it with the fog light relay. My fog lights started acting up and the AC started working fine. So check relays too. Start from the cheaper, simpler things then move on to the complex. I'd leave the starter for last. It's not easy to replace, access down there is terrible.