2. No. (You didn't ask why so it's because of the speed loss and the usual Smart TV wants the router inside 20 feet.)
3. Try WiFi Powerline Networking. There is plenty on the web but ....
You have powerline so you may need to replace it if it's getting old or the speed needs a bump.
Try this one?
Our modem and router are upstairs and at the other end of the house from the TV and there is no other place for them. We have a Cisco Linksys E1000 router (I checked and it didn't seem to need any firmware updates). We weren't able to stream Netflix from our Samsung Blue Ray player with any reliability so a few years back we used a Netgear 4 port Powerline 85 Adapter kit that supposedly mimicked a hardwire connection between the two. It did improve the streaming. However, the picture is getting increasingly pixilated. In addition, we cannot use the "On Demand" feature of our DirecTV connection because it's not picking up the WiFi signal at all.
1. Would a newer, more powerful router help? What kind?
2. Would a repeater help? What kind and where would it go?
3. Or ?????