Only in an academic setting. In real life, when you tell your child, "Pick up your shoes, make your bed, and put away your toys," you aren't yelling at him. You're just giving him a set of instructions. This is how an imperative like "Wash and dry your clothes" is often used.
The actual rule is to use "ad" for "a" before words beginning with the letter "a" and to use "ed" for "e" before works beginning with the letter "e", to break up the repeated sounds. But a lot of Italians don't follow all the grammar rules and some use "ad" and "ed" before any word starting with a vowel; not technically correct but frequently seen and heard.
I assume you mean "he", not "him". You tell by context. In an isolated sentence, you can't tell for sure, and I assume either answer will be accepted. But "vestito" is normally used for a dress, which is worn by females. The person involved in washing a dress would likely be its owner, who is probably a woman, so "she" would be a pretty safe guess for the subject.
The problem is that in Italian we have we call"soggetto sottointeso" meaning that the subejctof the action is bot mentioned but obvious. which in an example like this leaves plenty of room to interpretations...so it could be she/he/it but to make things more complicated could also be you ("tu") from the imperatif, like you explained in another reply in this thread
I translated "vestiti" as "suits", which Duo didn't accept for some unknown reason. To my knowledge, and according to previous lessons by Duolingo itself - "vestito" stands for both dress and suit, so it is only natural that I could also use the plural form for both meanings.
A romantic notion. I approve. But if Italians wanted to say that, they very likely wouldn't just say Lava e asciugo. That's too open for misunderstanding, and while grammatically allowable, violates normal collocation. They would likely at least include the pronouns to specify that, yes, they really do mean that she washes while I dry.
On a purely practical level, the exercise is clearly calling for the student to recognize that "lava" is second person present active indicative, and that s/he needs to conjugate the next verb to match. Allowing any word here that might possibly be construed to make sense would make the exercise futile and almost impossible to grade as "correct" or "incorrect". When the purpose of a sentence is simple and straightforward, as in this case, it's best understood as such.
I agree and had no doubt before, that it is this way.
I am german. But I have an italian daughter-in-law. And she told me: If in an italian sentence it is not clear, if the subject is male or female: it is always male. If this is correct, he and not she has to wash and dry.
Thank you for your comments.