Yes, it is possible. Whatever documents you have saved in your computer can be recovered regardless of the location or type as far as stored locally
That can be done, first you have to make sure the new domain name is available. If that so, you can modify the existing website the way you want and go with the new business/domain name
Operating system and software is not the only thing causes poor performance of a laptop or a desktop. Hardware component also should support the software requirments
It depends which part of the hardware damaged due to water and how hardly damaged. In most cases if that's a little spil damages can be recovered. Again it cannot be determine without anlysing the particular laptop
That could happen due to various reasons, software, nework connection, malware/virus, firewall. Without analysing it closely cannot tell you the actual reason that prevent connecting.