Does it work thru glass

The one I use works through the windshield, but I wouldn't try it with a rear window if it is polarized or tinted. 
 

Can you charge while battery is in use?

if you mean while driving? the charging system / alternator would put out a Lot more amps than this solar panel. it's meant to trickle charge the battery when not in use. Not substitute the charging system. if the charging system is working unhook the solar panel while you start and run the vehicle. 

Is this powerful enough to charge a 12 v marine battery and keep it charged? Also could it be used as a tender for 2 12v marine batteries in parallel?

I think that would be pushing it beyond it's limit, if in tandem. The tender is to maintain a charge, not charge. I have see that aircraft batteries have been maintained though. 
 

I want to mount this on my cargo trailer to keep the battery charged. Does this have a way of mounting it?

The frame around the panel has 4 holes one in each corner of frame comes with 4 screws too. 
 

Does the 12v come with battery clamps? Will this woeknro charge a trolling motor on a boat?

Yes is comes with clamps. And it will work on a marine battery, it will take a little longer to charge, seeing how it's a deep cycle battery 
 

How size panel wattage vs. battery capacity (Ah) just to keep it charged during long periods of no use?

If there are no parasitic draws off the battery the battery will eventually get fully charged and stay that way .The biggest deep Cycle in good shape can be maintained by the smallest solar charger. It might take a week of sunny days to bring up a discharged deep cycle battery with a lower output charger. 

he instructions say to attach the negative black alligator clip to the engine block. Can\'t you attach it to the negative terminal?

Yes, I think that if the battery is passing gas, old ones do, the spark could light up the gas. It’s a safety recommendation