do I have to do anything else when installting the new MP/DP/SUP
That depends. All of the normal prereqs apply for each of the roles. You'll need an install account as well in the untrusted forest and you'll need to open up the ports between this new site system and the site server as well as the system hosting the site's db. If you want to publish site info into the untrusted forest, you'll also need to open up those ports from the primary site server to a domain controller in that untrusted forest as well as extending the schema in that forest. Client push won't work unless you open up the ports from the primary site server to all of the potential clients (which I doubt you want to do) so you'll have to choose an alternate client agent installation method.
And will it affect the current MPs/DPs and clients? Or will these continue to use the certificate from the CA?
They will be unaffected.