Hi!
Thank you for the details, unfortunately I was not able to log-in with the username and password combination, it gives me an invalid username/password error. Can you please check that?
1. Can you please be more specific about this? If you mean you want to enable search within categtories, then this documentation may help.
2. I am assuming you want to replace the search bar within the site header. If the automatic replacement does not do that, then that search bar is very likely hard coded to the theme header files. You might have to ask the theme author on how to replace it, which files to modify.
If you want, you can add temporary FTP access as well, and I can check that for you. Although I cannot promise I can replace it properly, as it qualifies as a customization, but I will try.