If you click on the Armenian Church tag below, you'll see lots of threads, some of which have discussed attending an Armenian liturgy. Also discussed in one of the threads (I can't recall which) is the fact that we do have a final Gospel, and why.
The Armenian priest would probably give you Communion, but you are right in assuming this may excommunicate you from your own Church. So it's probably not a good idea.
We cross ourselves in the same direction as the Catholics. Otherwise, if you just act respectful and watch what everyone else is doing, you'll be fine. You may ask someone there if they have liturgy books to help you understand the liturgy.