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Fish hardly moving.
Some times laying on his back and trying to move.
When I've changed water it started to swim weired, like jumping up and down, then fell on the bottom.
What to do?

The ragged dorsal fin does not look like fin rot to me, it looks like mechanical damage. Could he have been beat up by some other fish? Or got stuck behind decorations? Has he jumped out of the tank recently?

The white spot on the middle of the side, on the other hand... is that on the fish or on the glass? If on the fish, that's some sort of wound or ulcer, and probably infected.

White spot is in the glass.
I think it is night fighting. I have only male orange spot in this tank and this one is female.
So, what I should to do to save her?

Damage from fighting or injury can become infected- either baterial or fungal. You should be able to see those things visually. I cant tell from your pic if the fish has either, but the front of the dorsal looks to have some white on it which might be out of focus something else or some infection.

At the very least I would move the fish to its own tank. I would start with just regular water changes to make sure things are clean. This will also get the fish away from a possible tormentor and the stress of that. You can dose Melafix which is a very mild additive which many use for help in healing non-serious injurys. Watch the fish and if it develops further symptoms, try to get a clearer pic of them and post again. You may need to medicate it.

I know I am new to pl*cos and everything but I was unaware that male and female pl*cos fought? I mean except for maybe jostling at feeding time?

What are your tank parameters? temperature, Ammonia, Nitrite, Nitrate, PH. What do you feed them? how often?

I have used melafix on my synos when they injure their top tail fin.

Yes, they are fighting over the cave or when female trying to enter male's cave to lay eggs or when male defending territory/fry.

Have you tried adding some more caves?
Whatever you do now, i'd suggest getting this fish out into a quarantine tank, and using clean well aereated water, see if you can bring her back to full health.
HTH
Martin

To echo previous points,

Isolate the fish,
Check water parameters -both in the main tank & the quarantine tank - make sure everything is top quality - this speeds up healing,
Increase the number of caves/territories in the main tank,
Melafix is a good bet to begin with, but you'll need to treat specifically if anything further develops.

This definately looks primarily like physical injury NOT finrot.

certain loricariids are relatively peaceful & most of us have seen a squabble which doesn't amount to much, however some are absolutely vicious with their own kind which can be magnified within the restricted confines of a fishtank.