Are the heroes allowed to have more feat cards than the total they start with, for instance if the hero has two melee and one subterfuge, and he opens a glyph, can he draw an additional card making his hand of cards four? Can he have more feat cards than the skill amount shown on his card?

i am pretty sure the maximum is 4

Tomb of Ice rules page 6:

"Unless otherwise stated on a player’s hero sheet, a player’s maximum Feat card hand size is four. If a player already has four Feat cards in his hand, he may still draw Feat cards when able, but then must immediately discard back down to four."