In American English, no, you cannot call typical weekends and typical days off "holidays".
a day for celebration when many people are allowed to stay away from work or school:
a national holiday
Thanksgiving, or Thanksgiving Day, is a public holiday celebrated on the fourth Thursday of November in the United States.
You can say holiday weekend, but this refers to weekends that coincide with an actual holiday, like Christmas Day Sunday, December 25, 2016. Holiday weekend also means a weekend that is preceded or followed by a holiday. An example is November 26-27, 2016. This holiday weekend follows Thanksgiving Day Thursday, November 24, 2016. This is often called a long weekend, since many people don't work on that Thursday and they take that following Friday off to have a four-day weekend.
In American English, when talking about days off, you wouldn't ask your friend "Are your holidays Wednesdays and Thursdays?", or "When are your holidays?", for example. Roughly, the first one asks "Are Wednesdays and Thursdays days for celebration?" and the second one asks "When are your days for celebration?" Instead, you could ask
- What/when are your days off?
- What/when are your off days?
- What days are you off?
When are you off? could work, but it has to be clear that you are talking about days. Otherwise, it could be interpreted as a question about the time that the person ends work. For example, When are you off? I'm off at 3pm. "What days are your off days?" works too.
You mentioned "what days are your weekend?" This question makes sense if it is understood from context that someone does not have a typical work or school week. So if you know your friend works on Saturday and Sunday (the assumed weekend), then you could ask "what days are your weekend?", "what's your weekend?", "when's your weekend?", "when does your weekend start?", etc. However, this usage is unusual, so I don't encourage it.