Why 'the cake' here is not translated as 'tortul'?
i'm not 100% sure, but my impression is that in expressions with "pe" (= on the), the noun remains indefinite, i.e. pe masă, pe tort, pe pâine
How come 'de' is not used here with 'pe'? As in "de pe tort"?
"tort" is the destination of your action, not the origin of it. "de pe tort" would mean "from the cake" basically, also as an adjectival phrase referring something that originates from the cake/locates on the cake in the first place.