Is this unit wheather proof.

Mine has bee outside for a year and survived hailstorms rain and winds up to 75 mph. It charges a deep cycle battery that is hooked up to a marine wash pump. 90 psi wash pump supplies rain water for the yard from a 600 gallon tank that recovers water from the roof. It works great 
 

Can this plug into the cigarette lighter port for charger?

i don't see why not

Have any of you seen there is reverse discharge from the battery to the charger?

I have never noticed this to occur. I've been using this charger for both of my bikes and it keeps the batteries charged. 
 

is there any way to attach suction cups to the corners?

There are 1/4 inch holes on all four corners 
 

can this work on the dashboard inside the car?

That is where I have mine, but remember direct unfiltered sunlight is always the best. I live in a condo, so I put mine on the dash for security reasons, and I use it to charge my Harley. 
 

Can this be put on one battery that is running a 24V trolling motor system on a boat while I am fishing? Or will I need a solar 12/24v controller box.

only for 12v battery