Since you will be finishing the cakes the next day, you can leave on the counter and cover with a clean tea towel (less lint). Make sure each tier has an appropriate size cake circle underneath it. You can use dowels if you prefer, but I find straws just as sturdy and a whole lot easier to cut (make sure they are not the bendable kind of straws. You can get a more exact cut with straws.
People think you cannot refrigerate fondant but I have had good luck with mine (I always make my own, so do not know how commercial fondant holds up in the fridge) My trick is to make sure I place the cake in the "driest" part of the refrigerator usually by the cripser, furtherst from the freezer section.
I always just store my cakes in a very cool room never put them in the fridge so it is just a preferance. You can stack them a day ahead as long as you support them. I usually use dowels but also have just tried the new poly supports and they are nice too and easier to cut. I use a pair of garden trimmers that I bought just for my dowels and they never leave my cake supplies. They work great for cutting the dowels. I have never used straws but there are a lot of people that use them with success. Usually I am doing 3 or 4 tiers so I go for a stronger support system.
If you are going to transport the cake you will need to run a sharpened dowel down through both tiers to keep it from sliding apart in transport. And yes you do need a cake board between the tiers. Be sure you cut all of your straws or dowels whichever you use the same length. What some people do is cut them to the height of the cake itself and if it is off at all the second tier will not be level so it is important to cut them all the same length.
You can finish your cake on Friday so all you have to do is enjoy Saturday too. I almost always finish the cake the day before it is to be delivered.
If the fondant starts sweating while warming up, place in front of a dust free fan.
Remember to turn the cake every so often to get every square inch.