Why Law of Supply indicate direct relation between price and supply?
You are confusing producer behavior and equilibrium.

If producers can sell at a price $p$ some of them will do so. Other producers cannot do so profitably at this price so the do not. At a price $p'&gt;p$ more producers can produce profitably including everyone who was already selling at $p$ so total supply increases. In this story the price was given exogenously. It was simply stated that the price is $p$ or $p'$ and we did not look at the reasons behind this. We simply stated what producers would do when facing certain price levels.

If given a price $p$ supply is larger than demand $p$ is not an equilibrium price. (An exception: it can be, if $p=0$. Would you like to buy some air from me?) You can say that this price does not occur, or at least not for a long time. As you state prices will probably decrease. In this story we looked at whether a price was actually likely given the market conditions (demand and supply). We did not simply assess what each side would do facing a given price but we tried to see if the actions of the two sides constituted an equilibrium.