Welcome to the community.
Premium hosting is offered by a separate company, iFastNet, so it’s better to ask them your questions about premium hosting at:
support.iFastNet.com
However, I might be able to answer a few of your questions:
1: Yes, your existing free ct.ws subdomain can be moved to premium hosting, but you’ll need to contact them to handle the migration:
2,3: Free hosting has a security system that prevents access outside of a browser. This affects previewing/embedding your site elsewhere and also means you can’t make PWAs on free hosting. This restriction isn’t present in premium plans, so both problems might be solved, but you’ll need to confirm that with iFastNet.
4: Are you referring to InfinityFree support or iFastNet support? InfinityFree offers community support through this forum, while for iFastNet, you’ll need to visit the link above. (Note: You’ll need to create a new account there.)