Hi there,
I see no one has taken a crack at this, so here goes.
Samsung did a poor job setting expectations about the use of the Gear S2. I have used a Moto 360 and the 360 (2015 model), and the watch functions as a notification panel more than anything else. the nice thing here is that it directly mirrors notifications coming in to the phone.
Because that's how Android Wear is designed, most people expect the Gear S2 to work the same way. Unfortunately, that is nowhere near the case, and it reacts differently between the bluetooth and 3G versions of the device.
Here's my understanding of the issue and the answer:
Making your email's sync is actually more than turning on notifications. I will have to say here that this is absolutely silly. You must open the gear manager, go to notifications and toggle them to "on", and then also toggle "limit notifications" to off. I also like to set "smart relay" to off.
Here's why: With all notifications on, the Gear S2 will only notify you about an incoming message/email/app when the phone it is connected to does not have the screen on. Samsung is assuming here that if the screen is on, the user is looking at the phone, and therefore, does not need an update on the Gear S2. Turning off the "limit notifications" feature turns off Samsung's assumption that you don't want notifications when the screen is on. The end result is that in order to get notifications you have to turn on notifications and then turn off limit notifications
The next issue is how you receive and interact with emails specifically.
If you use the standard Samsung email app, then you will be able to access all current emails received SINCE you connected your gear, and in my case, that DON'T come in while the Gear S2 is charging on the cradle. For some reason I don't get email from overnight when the device is charging. So, using the standard Samsung email app you will be able to use the Gear to navigate your current emails from your watch, read, delete, and reply. It works pretty well.
But...
If you use the Gmail App, or any third party app, then you will run into issues.The first issue is that the notifications for third party apps disappear from the Gear S2 when you clear those notifications from your phones notification shade. Try it for yourself. It's crazy. But while the notification is available on your Gear S2, you can interact with it just like you would expect. You can reply, delete, mark as read; it's a pretty crazy thing to think about, really.
I hope Samsung opens this up to more customization. Right now I feel stuck with using the Samsung apps, specifically the messages app and the email app. I would prefer to use the Google apps.
My work around is to to use the Gmail and Samsung's email app on my phone, but only turn on notifications on the Gear S2 for Samsung's Email app. This way I can interact with my emails on the phone through Gmail AND still get persistent emails on my Gear S2. The issue then becomes that since the Gear S2 does not sync my emails coming in while the device is charging, when I wake up in the morning I've got stuff on my phone that will NEVER show up on my watch... it's a bummer, but I deal with it.
As for the text messages, I just us the Samsung messages app. It's ok for me.
I hope this information has helped.