Question about Shore Power with a 100-150w solar system

I am building a teardrop trailer in which I plan to have a 12v system. The plan is to have 100-150w of solar, an MPPT solar charge controller, and a LiFePo4 battery. I also want to have the option of shore power to charge the battery using a 120v to 12v converter. My question is this: Can I run those systems together without damaging any of the components, causing a fire, etc? If not, what do I need for those systems to live in harmony?

Thanks

Correct to assume you are not running an inverter?

Not that it really matters, but on the face, you should be fine. Just make sure you run a charger (made for lithium) and not just a convertor.

Totally normal.

Since the converter could theoretically provide charging forever, I would ensure it doesn't hold the battery at 100% SoC and/or high voltage indefinitely. Lots of ways to skin that cat, including turning it off.