TIRE

Why are hard tire faster from medium or soft on any conditions ?????

Under certain conditions the hard tyre will be the go to choice but I don't find it being the one hit wonder and will beat everything tyre choice. The hards will get faster than softs especially if the temps aren't kept under control when the fuel goes down which probably coincides with the soft tyre going "off the cliff" grip wise towards the end of their stint. The effect of the hard tyre is probably magnified at this point as it is now running on less fuel with plenty grip left putting in consistent times while the other car has just fitted new tyres and a full tank of fuel for their next stint.

It doesn't beat all - I won in Spain last night in 20°C heat going Soft/Soft/Hard over a 50% race and my challenger went Hard/Hard - our cars looked pretty much level in development and not much to choose from in the drivers ability either.

Edit - doesn't help that you finished 5 laps - yes 5 laps ahead of your rivals in your last race.
Edit #2: Running hard tyres all the time requires a higher push level for pace meaning your engine ends up knackered quicker.