Questions on supply curve
Question 1 That's a reasonable way to think about it,but maybe missing out on a bit of nuance.  Realize that at any given price, the supply curve indicates how much WILL be supplied.  You are correct that if the price drops, the supplier will no longer be willing to supply that quantity of a good.  But likewise, if price increase, the supply will seek to supply a greater quantity.

Question 2 Yes, this is false. A change in price results in a movement along the supply curve and so increases/decreases the quantity supplied.  Supply itself is changed, meaning a shift of the whole supply curve, when faced with a shock, such a technological change.