1-No, you cannot do a Fiancee visa because you have accumulated unlawful presence by overstaying your visa. You will not be able to start the process until you actually get married.

2-While your parents name will be required on the application it does not affect them in any way. The office during your interview may ask as well but dont worry nothing will happen to them

3-You DO NOT have to go back to your home county, you were admitted to the US so you will apply to Adjust your status. You will need to remain married to your usc husband for 3 years and then apply for citizenship and only then will you be able to apply to adjust your parents status.

4-It is a fairly simple process but by this post i seriously think it will be a good idea for you to get an attorney.