OK, I'll have pity; we are here to help. But sometimes "help" means "help you to help yourself". In other words, prepare to do a lot of reading.
Free ports
Read the man pages for netstat and lsof. (And if you ask me what man pages are...

)
AI/roll forward
Given that you have discovered promon I will assume you know some basics about databases, or at least where a running one is and how to connect to it. It may be a little early for promon, but no harm, the worst it can do is confuse you (as long as you stick to the monitoring screens!).
After-imaging and related technologies are covered in the Protecting Your Data section of the Progress Database Administration manual. I suggest you go
here and download it, or even better, download the whole documentation library. It's not very big, by broadband standards. You didn't mention your Progress version, so be sure to refer to the product documentation version that is appropriate for you.
Before digging into the Database Administration manual, first read through the Database Essentials manual. It has some foundational material that will help you understand database storage internals, like blocks, clusters, extents, and areas. Once you have been through that, concepts like "high water mark" and other confusing terms you see in promon will make much more sense.
Broker, NameServer, Admin Server
"Broker" in particular is a term that, being somewhat generic, can have several interpretations depending on the context. There are database brokers (4GL, SQL, or mixed, and primary or secondary), AppServer brokers, WebSpeed brokers; they all perform similar functions in their respective areas, such as controlling client access to servers, however they have other roles as well.
The NameServer is a load-balancing feature that works with AppServer or WebSpeed brokers to allow you to create distributed, fault-tolerant applications. It is optional and may or may not make sense for you to use, depending on your deployment model. For example if you just run a single broker, e.g. in a development environment, it may not provide value.
I recommend that you go to the Application Server section of the documentation and read the Administration manual, for starters. It is important to first understand what these things are before trying to figure out how to stop and start them. Also, operational tasks like that will be different depending on your platform and the tools available to you (e.g. OE Explorer, OE Management, command-line tools). The appendix of the Administration manual has an overview of the various command-line tools, and there is an entire section of the documentation library devoted to OpenEdge Explorer / Management.
Finally, the Progress public
Knowledge Base is a pretty good resource for general questions. Give it a try.