i would say, in this context that ‘detergent commercial’ refers to an advert on television for laundry powder or dishwashing liquid where the home and marriage is perfect, and a smiling woman happily washes clothes and does chores with perfect makeup. The message of course is how happy women are to do the domestic chores, and the homes are perfect and conflict free. The wife is depicted as the ‘helpmeet’ to the husband. In today’s western society this is not the norm any longer with the majority of marriages have both partners with careers, and sharing domestic duties.

I would say 1) is when you are talking to someone and express a desire for them to play. There may not be an actual piano present, you are saying you want them to play, in general. Or it could be meaning - out of a choice of instruments, piano is the one I want you to play. 2) This is very similar to 1, and in fact it is just a manner of speech whether you say the piano or piano, although 1) sounds more cultured to me, as coming from one who is familiar with musical instruments. 3) Sounds odd. You would say this if, for example you were directing a mime and telling someone, now I want you to play a piano - meaning move your hands as if playing. A piano is too general to be used in a specific conversation about someone's musical career or choices. If there were a row of pianos and you were directing them to play on any of the pianos present, then that also would be appropriate. But it would rarely come up in a grammatically correct sentence.