I want to post a status update with all things I've tried the last days.
So first of all, it's working now. Not how I wanted, but it works . I tried to use a subdomain for Solder, yesterday I figured out that this caused my problem with Solder not syncing with the platform or the launcher. I can't say it was plesk's or my fault and I won't look into it anymore, so sorry for the folks that are running into the same problems with subdomains and plesk.
So I've tried it using my main domain. Some problems occurred there with Solder itself, I think that this was caused by poorly configured settings (apache, php, etc.). I messed too much around with them the last days. Knowing that and knowing that I will have problems with my subdomain I've tried to build everything from scratch on my second vps. Debian 7 minimal and a fresh manual LAMP installation. So everything worked fine, I've got no problems using my new setup.
After 3 days of work I'll leave it like it is now. My main server will stay for my minecraft server and as a community platform. Solder will be on my second server, which is only meant to run solder and nothing else.
A big thanks to Nentify who tried to help me with my problem and thanks for the hint with the web root .