Your webhosting issue
you can move your existing web site to a new host without starting from scratch.
First thing is to find your self a new web host.
The upload the web pages to that host using the control panel or ftp they provide.
Next step is more technical. You need to identify the company who provide your domain name and get the log in details for your account.
Then you need to find the names of the DNS servers for your new web host.
Next go back to your domain name account and point those DNS server addresses.
If the site is relatively new, it shouldn't hurt to buy a new domain name, which might be easier for you.
A few suggestions here:
Hope this helps.