Nightwing, Welcome to the Forum and Congratulations with your Epoch. In due course, I encourage you to Post a Review in the
Review Section and share the love. One Rule: Pictures or it didn't happen.
I plugged the charger in with the battery, and encountered 2 problems:
1. The charger is extremely sensitive. I need to be pressing it into the outlet in order for the light to turn on. As soon as I let go, it moves ever so slightly, and the light turns off.
2. The light is solid green. From what Ive read, that isnt normal.
With no In-Hilt Recharge Port, first troubleshoot I would suggest is ensuring the +/-'s are correctly lined-up from the battery to the actual Charger. If it still 'pops' out with little/no movement, to save you physically holding it down to initiate Charge, have you tried using a strip of Velcro or tape to keep Battery in place? If you don't want to go messing with it primitively, the recommended action is to send an Email to Customer Service (if you haven't already) where they will advise the best method to resolve the issue you're having. Allow up to 3 days for a response however in all likelihood, the reply will come sooner.
Your second query, my understanding is (and as written within the pages of the Forum) is Red=charging, Green=Charged and good-to-Go. If you are experiencing a solid Green lit-Charger LED, this appears consistent as once plugged in (without battery) it registers as good-to-go. With Battery in, it may still be Green as the Battery is Charged or because of the loose connection, it doesn't register the battery in place.
The matter may be as simple as a Faulty Charger or something entirely different. Wait for the response from Customer Service as further speculation is unnecessary. Kindly report back with the identified error and resolution supplied.