How can we say that one mole of a substance contains avogadro number of particles?
There's a nice Scientific American article that provides an interesting historical perspective on Avogadro's Number.  They go on to point out that one of the early accurate determinations was based on the first accurate measurement of the charge on an electron.  The charge on a mole of electrons (1 Faraday) had been known for some time.  Dividing the latter by the former yielded Avogadro's Number.

As to the volume of 1 mole of gas at STP, imagine the following experiment:

1) weigh out 1 mole of oxygen gas (32 gm)

2) fill a balloon with this weight of gas

3) attach a pressure gauge to the balloon and expand or contract the balloon's volume until the gauge reads 1 atmosphere

4) Immerse the balloon in a water tank and measure the volume of water displaced - 22.4 liters