Will this fit on my singer 111w155?

I installed this survo motor to my sewing machine table and do switch back and forth between my 111w155 singer to a Tecsew GC6-6, So yes it will install on any belt driven machine

Are the mounting brackets and rod included ?

Its been awhile since my husband installed it but we did not have to purchase anything to mount it. We did have to buy a new belt however. Wonderful motor

I know these motors have a way to set the speed but is that max speed and the speed is still variable up to max or do they only run the speed you set?

Yes, they will run from zero up to the max speed you have set. I just installed one on my machine, so I actually know what I'm talking about. The instructions you get with it are incorrect. For instance they say to press "R" and the display will read "U0", then press "M" repeatedly to get to the max speed you want (5 is 500 RPM, 10 is 1000 RPM, etc.) then it says press "L" to save the preset - there is no "L" button! Just press "R" again and it will store the preset. So far, I love it!