I have a two pronged question. 1. I live out in a very much country area so my ISP is sattellite. But after install. I don't

Solution
If it's a satellite connection, you're probably having that little gadget you mentioned as your main web access point; I'd bet that's just a powerline adapter, while the transmitter/receiver is somewhere outside.

Still, from that adapter you can connect pretty much "whatever floats your boat", provided the adapter can hold up the traffic.
A router would be the best choice for connecting multiple devices at the same time without too much effort (and wirelessly too if the router supports it), but for an open NAT status you need a static IP, open ports for the service you're trying to use and UPnP enabled.
If, however, your ISP placed a secondary NAT somewhere in the middle (mine does that, for example), you may have to ask them to...
Seen it got switched, we'll be who. After my satellite internet was installed I didn't see or at least recognize a modem. Just a very small device plugged to a outlet, with only two ports LAN and POE the device says carrier Poe adapter. Is this a modem?

I got internet for gaming and only gaming, xbox one. But have NAT strict issues, is this due to no modem? I bought a router n it gave off wifi connects fine(Belkin n600) but port forwarding n other handful of things won't resolve NAT issue.
 
If it's a satellite connection, you're probably having that little gadget you mentioned as your main web access point; I'd bet that's just a powerline adapter, while the transmitter/receiver is somewhere outside.

Still, from that adapter you can connect pretty much "whatever floats your boat", provided the adapter can hold up the traffic.
A router would be the best choice for connecting multiple devices at the same time without too much effort (and wirelessly too if the router supports it), but for an open NAT status you need a static IP, open ports for the service you're trying to use and UPnP enabled.
If, however, your ISP placed a secondary NAT somewhere in the middle (mine does that, for example), you may have to ask them to obtain a public IP as well, and some of them let you pay quite the hefty sum for it...
Otherwise, you're stuck at restricted or moderate NAT statuses.

In any case, having a moderate/restricted NAT status is going to provide issues only if you're trying to host something yourself in the first place.
You could try, if your router supported it, to set your PC as a DMZ device, but in short and simple words, that would mean exposing your system to potentially anyone on the internet, so it is highly unrecommended...
 
Solution
Yes your 100% right n the only person so far who knows what I've been talking about. The adapter is inside n reciever is outside, I can connect to xbox live fine but because of NAT issue party functions, chat, and even getting into lobby's are not working.
The ip adress as far as I know says is public (googled my ip) says public. And when I had my ISP service guy come out he sayed it was pub, n NAT in the receiver side was open. That "adapter" do you know if that is what's blocking my router from opening ports? And not have a "modem" I've dmz my xbox ip/ have upnp enabled, port forwarded all through my router but still no go.

Thanks for your time I appreciate your time and advice
 
If I assumed things right that's merely an adapter, meaning it's just a pass-through device. Whether it applies any kind of routing itself or not, it's a matter of asking your ISP's customer service.

I'm honestly not much into satellite connections, but setting a device as a DMZ should be the "Swiss cutting knife" of these issues; if that doesn't fix it there's most probably something else which you missed in-between or something that is not under your control, but for all I know it might just be how the satellite connection works...

Check if you have any firewalls active (windows has a default one and you can install a software firewall yourself, some routers have a basic integrated one, some ISPs force you behind one...yup, that's a lot) and configure them properly.

In any case, I highly advise you to use DMZ as a last ditch effort for the security risks it brings. Keep it down to port forwarding and UPnP; even if the former is still a security risk, it's still one (or a range) of open ports for ingoing, outgoing or both traffics, rather than ALL of them for both ingoing and outgoing traffic.