Using words from the SOWPODS word list, it's possible to solve Q1 and Q2 but sadly not Q3. I checked this by creating a graph of k-letter isograms, connecting words with no shared letters, and searching for cliques.
Five 5-letter words
Lots of answers, all using obscure words: e.g.
brick, jumpy, vozhd, glent, waqfs
vibex, fjord, nymph, waltz, gucks
bling, jumpy, vozhd, treck, waqfs
Four 6-letter words
Lots of answers, some using slightly less obscure words: e.g.
jawbox, kvetch, flumps, drying
jumbly, dwarfs, kvetch, poxing
jawbox, fledgy, skrump, chintz
Three 7-letter words
Lots and lots of answers: e.g.
stumped, flyback, whoring
mucking, batfowl, zephyrs
jordans, phlegmy, fuckwit
overply, dumbing, thwacks
Two 10-letter words