802.11n may indeed drop speed as distance increases. This is not unusual at all. There are tomes on the web about this. There is no one thing to fix and it's part of the system, not a defect or bug.
As to using your other gear to get a WiFi hotspot we can't start that conversation as there are no details.
Bob
So I upgraded my Comcast/Xfinity modem as they requested, and they sent me the modem/wireless gateway combo (I know, I know). I decided to test it out and I found a very peculiar trend: the further I get from the router/gateway, the slower my Internet goes. The network itself is unaffected, but when I run the Ookla Speed Test, the further away I am, the slower the Internet speed is, over 50% slower in some parts of the house.
I understand that the signal strength may not be as strong, but it shouldn't affect the actual Internet speed.
Has anyone else had this issue? Is there something that Comcast can do about it? Should I just have them disable their wireless gateway and go back to using my own? Can I bridge my old gateway with the Comcast network?

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic