4) You erase the profited and/or catastrophic gig because they are done. And you deal with the consequences.
Gigs are ongoing, hopefully gainful, "employment" for the Operator, they aren't one-shots... they're what the Operator
does... like a Gunlugger lugging guns; it's what the Operator specializes in... making the
moonlighting move is performing a specific instance of a job in that specialty.
If the Operator has "brokering deals" as a gig, she'd be known as a fixer, someone who knows how to put people together to get what they want, then she gets a cut... if they have "doing murders", they're an assassin for hire... it's what they're good at.
And you don't, necessarily, have to assign crew to each gig, the Operator could be doing it themselves, or with some crew, doing them all at once or one-after-the-other. Also, the Operator could take along another PC who could aid (or interfere!) with the roll to try and get things done.
Hope that clarifies at least part of this.