At least pushing it is free :)

I assume you mean radio frequencies, and the answer is basically none. A grounded fireproof safe is basically a perfect faraday cage.

EDIT: Ok, I actually have a pedantic answer for this. If you put a microphone on a device inside the safe, you can signal it from outside by sending it vibrations, and you could encode a message in binary and thus technically send it a “digital signal”. If you wanted to be a little more analog you could use Morse code :)

Probably yeah. A fireproof safe will be airtight, so the system can only produce as much energy as whatever reagents you put inside.

Where is “nothing is real, but good luck making use of that information”?