Regarding the power outlet, we don't see a direct reason why it might not work, but there are no guarantees that this power source is sufficient to source the required power for the server, the hub, and the router. We aren't familiar with the power source, and as such, we cannot give you a direct answer. Using unknown external power sources could overpower or underpower the devices, damage the hardware, and void your warranty. We would recommend consulting with a local electrical engineer to be 100% sure.
It's also important to note that we can't fully understand the country's grid and the distribution of cell towers or if the carrier would allocate you to a different city/state while driving around since this depends on the carrier configuration and cell towers distribution.
Ideally, Proxidize kit should be set up at home or office with good or excellent signal coverage for the modems to connect. Also, given that it is your first time using Proxidize, we recommend a normal static installation and maybe move it around later if necessary.