I added domain to Cloudflare and directed DNS to Cloudflare DNS. It works fine.
I do more or less frequent changes in DNS on hosting server by adding subdomains or other DNS entries not related to main web site. Some changes are done by hand but some are done by setting up some options on server that then adjust DNS as they need them.
Would Cloudflare sync with those changes on hosting server automatically or I have to manually replicate all changes from hosting DNS server to Cloudflare DNS?
No. As far as the public internet is concerned, which includes Cloudflare, the DNS on your host does not exist. Only the records in hosted by the authoritative nameservers found in the parent zone as published by the whois record at your registrar will be available. Once you removed the hosting provider nameservers in order to use Cloudflare, they lost any practical function.
Yes. Unless you have API access to your hosting provider’s nameservers and devise your own automation to replicate records into your Cloudflare account using the Cloudflare API, you will need to manually create any records in Cloudflare as necessary.