Yes, fan nut loosens in a clockwise direction. For a wrench I have successfully used a 1 1/4" combination wrench. If you have a 1 1/4, try it on more than one set of flats. I found that the nut isn't dimensionally perfect and while the wrench wouldn't fit one set of flats, it fit another.
Some have had good success without a holding tool and just giving the wrench a sharp whack with a big hammer or a dead-blow hammer. I had to make a tool the last time I removed my fan to do a water pump. I used 3/16" x 1 1/4" bar stock, drilled holes to go over the bolt heads and ground out a relief to fit around the nut with a bench grinder. If you go this route, be aware that the bolt pattern is rectangular and you want to use the LONG side of the rectangle for the hole spacing so that the tool is stronger. If you use the short spacing for the holes they are close to the relief and it creates a weak spot.
The reason I had to make a tool was because when I was in the first time to replace a thermostat I tightened the fan nut down too much and it was a bear to get off again. It's possible to wedge a long screwdriver between two bolts and brace it against the engine but when I did this the second time around I cracked the water-pump pulley.
The moral of that story is if you do get things apart, when it goes back together just snug the fan nut down a little bit, don't tighten it down really tight. That's the best help I can give you...