Used Tires start to lose speed at 50% (red). Not easy to get there with hard tires 20+ laps needed most of times.
Tracks get faster lap by lap Fuel Load Push Level and Current Tire Temperature Condition counts (not at blue and just a bit on red is ideal). Now if you compere with other players many more count;)
Used hards should be in the optimum temperature zone (manage this with your push level), new hards will be cool, tyres that are cool or too hot are slower than those in the optimum temperature zone, so, yes, they are faster. Just don’t let them get too hot or too cold.