For the few dollars a month that you pay them for hosting, it is very doubtful that they will waste any resources to investigate the issue. If you do not have access to the account with the registrar, you will have the same problem there as well.
Your friend can try contact the hosting provider. However, if the account is not listed under his name, I doubt the hosting provider will turn over login information to him.
There is no best hosting provider, only one that is best for you.
If you let us know what sort of budget and requirements you have, we can help to point you in the right direction
Most hosting providers to not offer free trials because they attract SPAMers. Just find a host with a money back guarantee and give their service a try