I setted up let's encrypt on a virtual machine. A dyndns domain points to this vm and it works all great. I can access the site by calling the dyndns domain and use ssl.
I have no experience with setting up ssl at all. Do I need to backup something? What if the vm is getting lost and I will setup a new vm and a new let's encrypt ssl certificate, which should work identically. Can I just rerun the let's encrypt wizard on the vm and get a new certificate or will I end up in an error, like their has been already a certificate been published and I need to restore the old certificate?
Yes, you can rerun the letsencrypt wizard and it will give you your certificate again, for as long as you control the domain. Remember that there are rate limits though and you can't just request over and over again.