1) "Have we got a computer?" and "Do we have a computer?" are both OK. It's a good idea to be familiar with both "We have an X" and "We've got an X". 2) "Is Anna on holiday?" Use this if you mean she is away from work and relaxing in another country now ("be on holiday"). You can use the US "vacation" in place of "holiday". If you use "have (got)", you mean Anna is working now, but has scheduled holidays in the future. 3) Like the first translation, "Have they got blue eyes?" and "Do they have blue eyes?" are both acceptable. Know them both, but if your teacher/textbook prefers one instead of the other, follow that. "Can anyone tell me if there's anything wrong with these sentences?" Your original question implied that there was definitely an error in each sentence.

Do we have a computer? Does Anna have a holiday? Do they have blue eyes? Can someone tell me what is wrong in these sentences?