Well if Mufasa has white dots and he didn't have them before i would not put him with another betta and i will recommend do not share anything between them in case he has something contagious. I don't know what is that white spot ? Is it something new? Is it fuzzy, cottony like? Sometimes white spot can be nothing or it can be starting of something. So i would wait and make sure white spot don't get bigger, fuzzy or spreads. And it always good be safe then sorry. If it something that is contagious then he can give it to your other fish.
Nothing wrong with 100% water changes especially if fish is sick.
I just was posting link in aokashi threas and i will post for you guys what can you treat bettas with daily 100% water changes. Not sure if everyone saw those links
see page 1; page 43 #422 and see page 42 and page 52 Amazing right!
another link which is amazing:
And i do for all my tanks 2.5 and 5 gall 50% and 100% a week . Don't have problems with my old bettas ever.