Great battery life and linux unfortunately are a hard task and linux support is often spotty for consumer devices.

Sticking to used business hardware is usually a good start, but you should check for compability issues nonetheless.

Yes, as the semantic of words is context dependent.

Hmm the prices on eBay really don’t seem that good to me in comparison to newer generations. I guess the power consumption will eat up any savings pretty quickly. Though this might differ for whole sets.

If you rent a VPS that might get you kicked, so check your terms first.