Virgin girl does need her father's permission for her marriage if her father is a Muslim and does not reject the marriage for un Islamic reasons. Your father does not need to attend your Nikah but he must agree on it if it is your first marriage.
There are certain cases when this condition becomes void like when you need the marriage to save yourself from sinful act, and your father is refusing the marriage for reasons which are invalid in Islam.
You have the choice to convert in secret, or to convert and tell them.
What is best to do really depends on your situation and on your relationship with your parents. If you have a close relationship, and they would be hurt if you don't tell them, or if they found out by accident, it might be good to tell them sooner rather than later. If you think it would just cause problems for yourself, needlessly hurt them, or endanger you (for instance, put you at risk of being kicked out), then maybe it is better to wait.
If you think you will be living a more independent life soon (for instance, living on campus at a university, or working and living on your own), it might not hurt to wait and tell them when you have more control over your life.
However, eventually you will (probably) have to deal with it. Although it might cause conflict and tension in the beginning, the best-case scenario to hope for is that it could eventually lead to mutual understanding. The real question here is when to go through that, and that is something you have to decide for yourself.
Also, keep in mind that it is difficult to keep secrets, and people often sense what we are hiding or find out accidentally.
You must do what ever you can to help your friend and protect her from falling in dangerous sinful acts. You must be completely sure that she is doing or going to do that sinful act. You can inform one of her family members who has more influence on her but not every one if you think that that member of her family can help saving her from sinful acts.
You should not lie about the cause but not broadcast it either, in case you increase the pain of the relatives.
Such deaths are not only hard for the immediate family, but also difficult to explain to others, as they may quickly be judgmental.
No, it is not necessary at all for you to inform people of the cause of death, and you can just say "he/she passed away, please pray for him/her." And if they have a follow-up question, repeat that sentence.
As you know, lying is haram, and so you should not make something else up, but just rather feel confident that you do not need to tell people this kind of personal information.
If they care and are concerned, they would just leave it at that, and respect your feelings and privacy and just do dua for the marhoom/marhoomah.