The ct.ws and wuaze.com domains were believed to be pretty stable. But court order could happen to any domain, there was nothing specific about these domains that means you should avoid them in the future. I’m not going to say “you should use domain X instead”, because other people might see that too, everyone would start using domain X, which results in more websites being on that domain. And more websites on the domain means more potential reasons to have the domain taken down, and more impact if that does happen. Like @Meishin said: the best way to avoid your free subdomain getting taken down is to not use a free subdomain.
Saying “you went through it” is a bit of an odd statement given that the problem has not been resolved yet.
You don’t need to download a backup. You can just add a new domain to your account and move the htdocs folder. Having backups is a good idea regardless, but it’s not necessary to migrate your website.
FTP usage is throttled at 3 concurrent connections, so if you set the number of concurrent transfers to 2 (which is the default in FileZilla), then everything should work smoothly. We only block IPs suspected of attacks (mainly trying to login with bad credentials too many times), so not sure what happened for you there.
try nic.eu.org and bet your luck, recently im able to register 40 free .eu.org domains so i believe they still active, or you can use other domain like digitalplat free domain