Yes, I use hot water. However, I also use a drop of clorox, a tsp of sugar (sometimes some aspirin) and then put the flowers in a cool, dark place to drink water for a few hours or overnight(but I condition all of my cut flowers this way).

Bacteria is the biggest enemy of any cut flower. Change the water every day and if possible, clean the container or put just a drop of the clorox in everytime you add new water. Keep your arrangement out of a hot, sunny location.

Yes, I find all of the above makes a difference.

Yes I also cut into hot water, the hottest I can get about 125 degrees. This helps hydration and sets the bloom. I leave in the hot water until it cools down and then put in the floral cooler.