Yes, that is no problem. Our shared hosting (referring to non VPS/Dedicated Servers) services use cPanel or Plesk which is the most common control panels. If your current hosting doesn't use these or doesn't use a control panel at all, then we can manually transfer all your website's data.
We aim to have basic websites transferred within 3 hours but transfer time depends on your website's size. For example, many bloggers have a large amount of images which could mean they have files using up to 30GB of disk space, so it will take longer to transfer this amount of data. We will keep you updated during the transfer process.
No, we will migrate all your website's data to your new hosting package, and when you are ready you can change your domains nameservers which will make the swap from your old to new hosting. We recommend not cancelling or turning off your old web hosting for 72 hours once you have made the nameserver change.
No, we don't limit you on the number of sites to migrate. If you have any special migration cases such as 100's of GB of data then we recommend contacting the sales team as this may require extra time and need to be quoted for. Most websites are under 10GB and we do not limit the number of sites in these cases.