Is it possible to transfer my website to another web hosting company with no downtime?
Answer:
It depends on whether your website is static or dynamic (has a database that it updates regularly).
If it's static, then it's very possible. Simply store a copy of all your files in the new hosting server, then update the nameserver in your DNS setting to point to the new hosting server's address.
If it's dynamic, it's a bit complicated to make sure the database in the new hosting server isn't missing any update done by user accessing the old server.
The reason such synchronization issue may occur is because when you update the nameservers, it takes up to 48 hours for all nameservers around the world to propagate the change. And between the time when you make the change and 48 hours afterwards, some DNS servers will have updated the changes you make while some haven't, so that some users will still go to your old hosting, while some have gone to the new one.
This is not an issue with static websites because it doesn't matter which hosting server user goes to, the content is the same anyway. But for dynamic sites, some updates will then happen in the old hosting server and some in the new one. Synchronizing the 2 databases will be a huge task, especially if you have a busy site. So people usually would rather go with bringing the old server down.