1. There are MANY sticks like this one.
Remember these are plentiful so I only note one and you find the other 300.

2. For that your best connection is Wireless HDMI. Remember that even with that, there is lag that means NO GAMING! Wireless HDMI solutions are again, plentiful.

And yes, you could use the Samsung wireless LAN adapter (WIS09ABGNX, WIS12ABGNX) but I prefer other solutions for the price and longer range. The Samsung wireless LAN adapter (WIS09ABGNX, WIS12ABGNX) seem to be about 20 feet (7 meters) on average. You can do better for less money.