thanks for evaluating DreamHost, I'll try to give you an answer
One thing I noticed in your request is that you don't say how much traffic your sites use, and what your current package is providing: are you using a VPS now or a shared hosting account?
If your sites don't have much traffic, you may be able to run all that on a Shared hosting plan and see if that's enough... If not, you can grow to a VPS or dedicated, eventually. You may want to start by migrating one of your services at the time, to make sure the Shared hosting plan is a good fit.
You'll get free SSL certificates with all DreamHost domains, and you can add CloudFlare basic DDoS protection to your sites, too. See https://www.dreamhost.com/partners/cloudflare/
DreamHost doesn't use cPanel but has its own control panel (you can read about its features and see some screenshots on the Knowledge Base https://help.dreamhost.com/hc/en-us)
To identify which databases are being used, you may want to check the configuration files of the services you're running. Go inside myBB, phpBB and MediaWiki and look for the database names specified in the various config.php/ini etc. Then backup the databases that are not listed there, and remove them one by one, check that all your sites are still working and continue until you have only the databases you're actually using
I hope this helps you get an idea of DreamHost capabilities.