Because I am looking to move to Cloudflare, I currently have a SSL for example.com but not for www.example.com, will this be fixed if I move to Cloudflare?
And what happens to the SSL Certificate on the server?
The default Universal SSL will give a certificate covering example.com and *.example.com so all first-level subdomains will be ok. If you need second-level or deeper subdomains (such as sub2.sub1.example.com), then you will need to use the Advanced Certificate Manager.
You must keep that (and keep it updated) to ensure that the connection between Cloudflare and your origin is secured. Make sure your SSL/TLS mode is set to “Full (strict)” or “Strict” only in the dashboard here… https://dash.cloudflare.com/?to=/:account/:zone/ssl-tls