I agree that is "appears" to be a bacterial infection on top of demodex. But, the only way to tell is to have him checked.
Localized demodex can sometimes be treated topically. In rare cases, some that are localized will resolve on it's own (if there are one or two spots). But generalized demodex is a severe
Not saying this to scare you, but I have seen puppies that have nearly perished because the demodex just continues to suppress the immune system and then bacteria take hold. If there is enough access, the bacteria can become systemic (thru cuts and wounds).
I'm not going to get into a food debate here, but I will say that changing the diet will not boost his immune system right away (eventually, it will absolutely do wonders for your dog in so many ways
). Board certified dermatologists will tell you that you must be on a diet a MINIMUM
of 8 weeks for a change to be noticed. More recently, many have ammended that to 12 weeks.
So, although I agree a better diet is only going to help, it will likely not make a major impact for several weeks to months.
I am sure $$ is tight, as it is for all of us these days. But, honestly, the puppy needs
to be seen by a veterinarian so that a proper diagnosis and treatment plan can be established.