If you can think of a ship, i will answer these questions for them

who cooks normally?:

     They both take turns cooking, as they are both very domestic. Peeta taught Phox how to create frosting from scratch and many other things as well.

how often do they fight?:

     Rarely if at all. They both tend to work out their issues and have hardly ever resorted to yelling.

what do they do when they’re away from each other?:

     Teasing which consists of brushing up against each other, flirting over breakfast, joining each other in the shower and neck kisses. Neck kisses demolish Phox.

nicknames for each other?:

     None at the moment. 

who is more likely to pay for dinner?:

     Peeta will always insist on paying the bill, though Phox is stubborn about it. 

who steals the covers at night?:

     Phox does, but Peeta doesn’t mind. He prefers to sleep without covers. 

what would they get each other for gifts?:

     Peeta gives Phox things he can use around the house, and stuffed animals. But yes, they would.

who remembers things?:

    They both have excellent memories about the events of their relationship.

who cusses more?:

    Neither, they’re both soft spoken and rarely curse. 

what would they do if the other one was hurt?:

    Nurse each other back to help. They’re both very domestic, as said before. 

who kissed who first?:

    Peeta kissed Phox out of whimsy, and was glad he plucked up the courage to do so.

who made the first move?:

     Phox, on accident when he placed his hand on Peeta’s thigh without thinking. 

who started the relationship?:  

     They both came to an agreement that being together would be fun, even if they weren’t too sure about the prospect of a relationship.