Codes P0138, P0455 and P1687, fuel related?

Yesterday my fuel gauge started reading full only. After I filled it, I drove around all day for work, and it just read full. I thought maybe the float is stuck but because I don't feel like cutting a hole in my bed, I thought maybe I can get lucky. So, I started to reset my cluster when I noticed three new engine codes p0138, p0455, and p1687. Are these related to my gauge issue? How can I confirm? Also, what can I do to just throw some money into it and get it over with? Can I just buy a fist full of sensors and say screw I'll just change them all related to the codes?