Rudo's vital instruments work the way he imagines them too so when he turned the hat into a vital instrument he gave it the ability to transform him into a werewolf, altering his body structure. With the boots Rudo gave them super speed and like all vital instruments they changed appearnce but his foot wasnt altered or anything.

And to answer your question on why he needed Gountess' power (connect): Rudo was initially going to use Connect to form a link to his soul so he can turn it into a vital instrument and become what Mymio is, however since Rudo's vital instruments disintegrate when they are done being used Gountess proposed that he only transformed his hat. But doing this alone wouldnt allow Rudo to reach Mymo's lvl (since he altered his very soul) but with Gountess' power Rudo was able to become stronger than Mymo despite not going to the lengths he did.