You totally can. I've seen cases a rat gnawed a circuit breaker and blacked out a DC. Fires too. It's not an industrial manufacturing facility. Computers can just be shut off and on. There's also nothing needed to bootstrap the other parts like cooling etc.

I totally can. And if it's powered by solar (low inertia) there's less obligations to supply side, solar panels will just get warmer a tiny bit.

Batteries exist, and are getting better all the time.

Datacenters literally have UPS power supplies to let them gracefully shutdown and start up.

A 4 hour grid battery and a weather forecast would easily let a training run follow energy availability.