That depends completely how you have configured dragoncloud and shop.
You can set it up to work either way around - which do you want ?
It works with dragon-cloud.ddns.net/dragoncloud because you have also configured your setup to work that way. Without seeing your configuration, and knowing how you’d like it set up, I can’t say if it’s correct or not. This is nothing to do with SSL certificates though, this is purely domain configuration and setup.
That will change your IP at no-ip, however some DNS servers will not change straight away, so your local ISP’s DNS server ( which you probably use, or your friend uses a different ISP, with different DNS servers ) may not update for a day.
Before I can do that, you need to decide if you want to configure your sites to work on subdomains ( shop.dragon-cloud.ddns.net and dragoncloud.dragon-cloud.ddns.net ) or if you want it to work on the main domain ( dragon-cloud.ddns.net/shop and dragon-cloud.ddns.net/dragoncloud).