You should only need to establish the connection once. After that, communication is bidirectional. I speculate that your fault is related to creating an outbound connection when you already have an inbound connection established with same gateway, but -disclaimer- I have never tried this myself.
I recommend that you always create an outbound connection from the Edge --> Full gateway, and have only inbound connections (from Edge gateways) at your central gateway.
Regarding setting up the remote alarm pipeline, verify that you have correct settings configured for Remote Gateway Name under Config > Data Sync > Settings. IIRC, after you set up Edge sync services correctly, you should be able to pick a remote alarm pipeline on any of your tags. If not, you might be blocked due to Service Security settings on the full gateway.