I have been having 2 separate, but quite annoying issues with the car lately.

1. The gas mileage has become awful. I used to get up to 500 miles on one tank on interstate, now I am in mid 300s. My guess is the Knock Sensor, but with the freezing-*** winter, I didn't want to play with it, but now that it is getting warmer, I am going to check the codes.
Could there be another thing to look for that can cause this?

2. The car will not start normally when cold. It started happening about the same time as the gas mileage (maybe the issues are related???). First I thought it was because of the cold temperatures outside, but now it is in the 40-50s and it still wont start. I have to give it gas after the engine turns over and hold the pedal for a few seconds and then it is all gravy. Even if I stop and restart the car after some time it starts fine, as long as it hasn't set for too long.

What could it be? Could the issues have the same source? Can Knock Sensor be responsible for them?