There are save files for each location you can download at
http://machinarium.net/forum/index.php/topic,1274.0.html so you could download one for the next room and go straight there. I'm assuming there are instructions somewhere.
I don't get the question about the save slots, unless the answer is "click on a slot in the save option to save, click on one in the load option to load."
The patches should already be installed if you only downloaded the game recently.