If the power goes off, the Pi will go off. When the power comes back on, the Pi will restart and NodeRed will also restart. If you have a timer, for feeding, let's say, that feeds for 10 minutes every hour (starts at 8:00 AM and ends at 8:10 AM, starts at 9:00 am and ends at 9:10 AM, etc), the power goes off at 11:40 AM and comes back on at 1:15 PM, the timer will restart at 2:00 PM and stop at 2:10 PM.
It is my understanding that the timer within NodeRed can be programed with either start time/end time, or immediate start and duration (on for 12 hours/off for 12 hours) have just started looking at it. Do you know much java scripting? It appears that it can be configured through a settings file (settings.js). I would take a look at the users guide, especially the "Configurating Node Red" section.
Just started getting back into programming (did a fair amount of C/C+ many moons ago) but it seems fairly straight forward
I reread what you had posted and I was confused (which wouldn't be the first time, by any means) I wanted to see if I understand. First off, the Pi never "shuts off" the timer will, but not the Pi. That would be like turning on your phone to check for calls, turning it off, then turning it back on 15 minutes later to check again. Second, it sounds like you want to start the Pi from your compressor, to start your pump, to start your compressor. I was really confused. but like I said before, not uncommon.
There are "Hats" for the PI that will sense all kinds of things like humidity, temperature and pressure. I would look into something like that, that may be able to be incorporated into NodeRed so that the pressure reads low, starts the pump, and then starts the compressor either at a certain fluid level, pressure or time. That is one of the nice things about Linux and open source, if you have a problem, someone has probably written something to fix it, because they had the same or similar problem.