Well, if you come home and have fowl yourself, you would wonder whether your wife/husband was cooking a duck or a chicken - one of the few cases in which this question would make sense to begin with - and maybe you wanted to imply, that the only options she/he had, were cooking a duck or a hen, since you wanted to keep the roosters you had for breeding. A situation that is not at all unrealistic at my home. But maybe it is a bit stranger to say something like this in English, even in a rural context. After all, animals tend to change their name in English, when you eat them. I for one had this situation in my head, and since курица is the only word for "hen" in Russian I translated it just like that.
It is simply a spelling rule that the ты form of verbs is spelled with -шь. The soft sign at the end has no effect on the pronunciation.
Similarly, I believe that it's a spelling rule that feminine nouns ending in hushes are spelled with -ь (e.g. ночь, мышь), while masculine ones are spelled with just -ч, -ш, -щ, -ж (e.g. муж, нож, луч, душ). See the bottom of https://www.duolingo.com/skill/ru/Possessive-Modifiers-1 .
Well, these days when you can get frozen, pre-dressed chicken, I imagine that your sentence would be less common. But in English, you would normally say "plucking", " skinning", "de-boning", or " cutting". You might say are you preparing, but like I said, it's a bit less common.
would I use вы instead of ты? What exactly is the difference between the two?
Use ты when you are speaking to one person whom you know well or would address by their first name (relatives, friends, children).
Use вы when you are speaking formally (to a person you would address by their last name), e.g. to a stranger, or when you are speaking to several people at once (regardless of how well you know them).