Fuel flow

1. Why does fuel flow increase with airspeed? I was climbing to 4500 feet in a Cessna 172 with full throttle. I already leaned the mixture after 3000 feet. My climb speed was 75 knots. At 4400-4500 feet, just before I started leveling off my fuel flow was 7-8 gph. I leveled off at 4500 feet and I left the throttle at full to increase my airspeed and the fuel flow increased to 10 gph at 100 knots. Why if I didn't touch the throttle or mixture control after leveling off?
I know that the propeller RPM increases with airspeed but if I left the throttle valve the same before and after leveling off, shouldn't the fuel flow be the same?
2. Also why is the fuel flow above 3000 ft MSL lower when the mixture control is at rich than when I lean it a bit? Shouldn't the fuel flow always be higher when the mixture is full rich.
I'm refering to FS2004 up here, I don't know is it like this only in the sim or also in real. It seems that in FS2004 fuel flow increases with engine RPM and not only with the throttle and mixture.
I know that the propeller RPM increases with airspeed but if I left the throttle valve the same before and after leveling off, shouldn't the fuel flow be the same?
2. Also why is the fuel flow above 3000 ft MSL lower when the mixture control is at rich than when I lean it a bit? Shouldn't the fuel flow always be higher when the mixture is full rich.
I'm refering to FS2004 up here, I don't know is it like this only in the sim or also in real. It seems that in FS2004 fuel flow increases with engine RPM and not only with the throttle and mixture.