I'm looking to stay in Ibiza on 14/November for a day but I read that maybe the most beaches are closed, and the island is desert, the market is closed on this month with a very bad weather, but I don't know if it's truth. As turist, should I avoid the island on this month?
most beaches are closed
Beaches are of public access. They are not "closed", you can go as you want. The difference will be that there will be no services like lifeguards, beach bars and restaurants and the like. But most probably, it will be not very cold but cold enough that you will not enjoy taking off your clothes to sunbathe or take a bath.
the market is closed
Believe it or not, apart from tourists there are people who actually live in Ibiza and they do their shopping all the year round. That said, november is low season so many tourist ammenities and facilities (hotels, discos, bars and restaurants) will be closed. But there will be enough left open to avoid starvation.
month with a very bad weather
In general it is not often stormy/rainy (but there may be some storm or rain), but it will be, without doubt, far colder than July (bless God). Anyway, you can always check any weather service.
In conclussion: you can go to Ibiza, but you will get some holidays that are nothing like the ones you would have in Summer. They will be way more quieter/calmer. I would avoid beach hotels and look for hotels inside towns.