1) I was wondering what the conditions are for a Virgin to get into a muta, temporary marriage. I read on Sayed Sistani website that she needs to be independent. Could you be more specific about what it means exactly to be independent in this case? For example, a woman who lives with only her mother and brothers works and has her own income and is economical independent and does even pay rent at home. Her dad is not providing for her economical and he hasn’t done so in the past years. This is considered being independent but how does religion look at this situation. Does she still need her father’s permission?

2) Can she have the right to do it if she ask her dad to give her permission to marry whoever she like and she can decide on it?

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1) Independence here means that her father is not getting involved in her marriage decision, and he left it to her to do what she wants. In such case, S. Sistani says, she still needs to get her father's permission as obligatory precaution.

Financial independence does not give the girl the right to marry herself, unless her father left the matter to her and did not interfere in her marriage decision.
And even in this case, the father’s permission must be taken, as precautionary act, according to Sistani.
Yes, she can refer in this precaution to S. Muhammad Saeed al-Hakeem, so she may get into temporary marriage, on the condition that no intercourse is practiced. You can refer to S. Hakeem by just making intention that you are referring to S. Hakeem in this particular issue.

2) If he gave her the permission for the temporary marriage as well, the yes.