The exhaust brake is a much more technical way of stuffing a potato in the exhaust pipe. :)
The turbo in your truck is much like a fan, but it spins at very high rpm. Older design turbos were fixed vane designs, meaning the "fan blades" were of one shape and could not be adjusted. They were a compromise between fast "spool up" and the ability to flow hign volumes of air. Fast spool up reduces that delay between pedal down and the rush of power that sets you back in your seat. Small turbos spool up fast, but at the expense of being able to flow large volumes of air for high horsepower.
Large turbos spool slower, but support higher horsepower because they flow more air.
Always a compromise.
In comes the "VGT" or variable geometry turbo. What this does is, by being adjustable, it can spool quickly, and open up once up to speed to slow more air - best of both worlds.
Manufacturers then realized that by essentially "locking" the transmission to the engine and closing off the turbo vanes (the adjustable part) they could reduce the engine's ability to flow air, cause a restriction, and slow the truck. In comes the exhaust brake.
Why people say to use it often is because they have a tendency (over long periods of time) to get sticky by getting clogged with exhaust soot if not "excercised". Especially the first designs. Manufacturers then installed software that would exercise the vanes (move them through their full range of motion) without the driver knowing to keep them from sooting up. I am not 100 percent sure, but I don't believe it's as much of a problem as it used to be.
On to your next question about tow mode.
What this does is again eliminate a compromise. Manufacturers used to have to make the computer program that controlled the transmission work well in all conditions. Towing or not, mountains or cruising the flat terrain with no load.
Now with the tow mode, by prezsing the button, you are telling the trucks computer that you are goingto be hauling a load, and it would be best if it switched to the computer program the enegineers put in to be best suited for towing. Firmer shifts, less heat huild up, and more aggressive gearing down to hold back the load.
Couple that with the exhaust brake function, and you have a good 1-2 punch.