Can I leave solar panel on the dash of my van or front seat during the day?

Don't see why you couldn't. Mine lives outside year 'round on a post for my electric fence charger (the panel portion). Just don't think you'd get the direct sun you need long enough to do much charging unless you keep moving your van as the sun moves. 
 

Is the charge controller portion of the kit waterproof as well or does it have to be mounted out of the weather?

I would say no, the wire attachment area is very close together also so putting the wire in is difficult to keep the fine wire from touching the wrong terminal. SOLDER the ends first for a trouble free long lasting connection 
 

Can i mount this to my van roof and keep the battery charged

you probally could, but you have to build a frame to set it in and secure it to the roof so it doesn't get blown off+ road jarring might affect this. 
 

How well does it do in rainy weather as far as weather proof?

I’ve had mine installed for two years in the weather. No fogging or signs of leakage. Wipe off a little dust, and it looks like the day I unpacked it. Still works great. Deep cycle battery is also 2 years old. It’s maintainance free so I have not had to touch anything for 2 years. 
 

Will this charge a car battery?

Yes it would but it would take a really long time.a 20w panel will only make about 1amp. It will be almost like a trickle charge. Also you would need a charge controller 
 

will this maintain a charge on a farm tractor over winter?

This is a solar energy collector, not a battery. You will need to connect to a battery. Your question is impossible to answer without more info... Size of your battery, number of sunny days, how often your tractor is used... 
 

How do I extend the cable length from the solar panel to the battery? Need like 35 feet of cable about. Thanks

make a cable yourself and you can put your own ends on 

will this work lead acid battery

Yes, according to directions. The panel came with the necessary electronic controls to charge a lead acid battery. At 3 amps it will be a slow charge. I have not charged a battery with this solar panel, but I have been using it to power a 12V evaporation cooler and it works perfectly. 
 

Will this charge just one battery or can it charge both batteries for travel trailers

We have a RV, class "C" motor home and I use the solar panel to charge two six (6) volt house batteries that are wired together in a series, as a logical 12 volt battery. 
I connect the solar panel terminals to each battery, the black (negative) to battery one and the red (positive) to battery two. 
Hope this helps? 

What watt kit would be best to maintain my 12v battery on my RV for storage?

I would recommend the same size about the same length that's on there. Use a good single wire type connector. Any extra length you have to watch your amps they can drop with bigger and/or longer wire. 
 

what kind of lights should I buy? I want to light the inside of my shed

Led is your best bet. Get a automotive or lawnmower battery to charge. And run a inverter to power your light or charge weedwacker battery ect ect. Works pretty well. 

Can this unit charge a 12V battery that powers my boat lift?

Thats what I use it for. works for me. 

Can the panel be mounted to a pole?

No reason why it couldn't, you'll have to fabricate a mounting system.