My pump is down and is "hopefully" being repaired. Our pool has been at a stand still for 3 days now, but I did just start up the submersible pump today to move things a bit. While talking to the PS today about getting the pump repaired, they suggested I could put Non-Chlorine shock in the pool even though the water isn't moving. That would help things not get worse, basically.

I already have a bunch I bought last year before realizing I probably didn't need it.

Would it help?
How often should I add it?
Will it affect my FC levels (which I haven't even tested yet because the water has not gotten a chance to circulate since opening.

I would add bleach, by pouring slowly while walking around the perimeter of the pool, and then immediately brush the entire pool. The brushing will provide enough circulation to mix the bleach in.

Non-chlorine shock will help whatever chlorine you have in the water last longer, but non-chlorine shock won't kill algae. Overall, it isn't a great choice.

And non-chlorine shock is around 3 times as expensive as chlorine in terms of the same equivalent FC amount. Non-chlorine shock will also register as Combined Chlorine (CC) unless you use a special interference remover for that test.