No. No mixing. It's important to give her the proper dosage. The way I do it is to dump the powder out of the capsule onto a plate. Divide the powder into two little piles as equally as you can. Don't fret too much about it, though. A short dose today will be compensated with the larger pile...
Left over people antibiotics will work until you get the fish mox. (also called aqua mox). Usually, as the others have pointed out, these laws against over the counter pet antibiotics do not include fish meds as these are labeled "not for human consumption". Most online pet pharmacies will ship...
Lice, unless a chicken has an extremely heavy infestation for a long period shouldn't cause a chicken to be sick as lice do not suck the blood as mites do. Lice feed on dead skin and feather dander.
I would be concerned something else is going on with this hen besides lice. As @coach723...