Do I need 10 gauge power cord if I have 10 gauge from panel?

Do your mono blocks have overload fuses? Most do.

If so, what amp fuses are they supplied with?
3A?, 4A?

14 gauge is rated to 15A so you should be good to go…

Jay’s Audio has many demos showing differences between pc’s in sound. Search them out if you want to. Synergy and everything makes a difference are key mantra’s that play out in practice. I have also upgraded cables from my sub board to my outlets and will be matching them to my highest grade cables in this new set up.

I would try and match your cords to your wall supply so you are not effectively choking off the available supply with resulting differences in resistance inductance and performance. Still you may need to try various cables to get the synergy you need.

14 gauge for your source (s) and 10-12 gauge for you amp (s). 

Does "negatively impacting" the sound mean "degrading" the sound? Just wondering, here in our post-verb universe.

Cable discussions here tend to come down to beliefs. I believe a cable can improve the SQ. Or, I believe it can’t. But this issue is not about believing. Just listen and hear for yourself. No belief is required. Reshelving fees make us want to know what’s possible. In the end, your ears tell the truth. While at an audio show, a manufacturer swapped out four of their power cords. Frankly, I was a little pissed that I heard differences. I wanted to hear the same SQ from all the cords. Even though the SQ was unmistakeable different, I chose not to spend $1,000 on a power cord not because it wouldn’t help but because i have some ceilings on my spending. You can believe me or not but there’s no reason for belief to enter a cable discussion. As for the science behind it all—it doesn’t matter. You hear it or you dont. Whatever your answer is, you’re right.