Dual Ethernet Ports on new Motherboard will help with streaming?

There is no speed advantage to dual ethernet ports, they are helpful for using your computer as the "hub" of your network. Theres a lot of different ways to configure it (2 networks, server, firewall, etc), but in the end you will not gain any speed advantages, just the ability to do a lot of different network setups.

It doesn't really work like that, your network will deliver its max bandwidth based upon your hardware all the time, unless more than 1 piece of hardware is taking up bandwidth. IE when my PC is the only thing plugged in to my network I have no problem pulling in 50-60 mbps or more. But if my phone, laptop, etc are going I start to lose out a bit. So plugging 2 cables in just splits the traffic between 2 ports, but doesn't give you 2 50 mbps connections, and your computer and router do their own jobs of dividing up traffic, no need for you to. Your downloads running at 10 mbps is likely more of a limitation of the network you're connecting to (whoever youre downloading from), not your home network. The best way to know if your connection is the best it can be is to run speedtest.net and make sure you get that 50 mbps. For the record when I download from Steam I rarely get more than 9-10mbps, Playstation Network noticeably less, and my network tests out to 60 mbps regularly. Their bandwidth is as important as yours.

That said there are routers out there that throttle network traffic. I was talking network with my boss a couple months ago as I was looking for a new router for my new much larger home network I was building. He recommended the one he has as "good enough". I did some research and found out that it limited traffic to 25mbps. Had him do some tests, then I got him to buy the one I settled on. He was so pissed he wasted so much speed for so long!

There is one way that you could use this to increase your bandwidth and that would be to have 2 separate internet connections in your home (ie 2 drops, 2 cable modems) then both ports would be able to fulfill requests at the same speed, so in theory you'd double your bandwidth (assuming everything plays along nicely).

This also highlights the problem with plugging 2 cables in to your router to the PC, in the end the line into the home is the same, so as I said all you'd be doing is splitting your traffic over 2 connections instead of 1.

Really the best things for this is for setting up a home network (and using your PC as a router) and also redundancy in case of a failure (and I've rarely ever seen one fail), or if you have a huge amount of cash to burn (like pro gamer status) and can afford 2 internet connections in your home.