I know this question has probably been beaten to death, nevertheless I hope
you will still indulge me.

During a power outage, which occurs frequently in Florida, I would like to
use a battery to power some communication gear. Although the battery is 12v
and not 13.8v, I think that the gear will still work OK (hopefully).

Question 1. I believe that car batteries have a low internal resistance
because their primary function is to provide a lot of current for a short
time. There are other 12v large battery types that will last as long as a
typical car battery. They are designed not to provide peak current, but to
supply steady state current for a long time.
For the life of me, I can't remember the name of those type batteries so I
can't do a google to find a supplier. I hope this is making some sense.

Question 2. Where can I find articles & schematics for a solar cell to
provide a trickle charge for the aforementioned battery?

Thank you very much.

Cordially,
west