Make a mash tun out of just about any cooler...link below is a simple one
Simple All Grain Brewing - German Pilsner
Or search for Denny Conn regarding cheap batch sparging...wealth of info there.
I doubt the side burner of a bbq will be much help to ya??
You can also use several smaller pots stove top to make the 5 gal batch, or do smaller batches stovetop. If all you can do is 2-3 gallons you could do a texas two step sort of thing where you make wort two days in a row and add to the fermenter as it is available.
Unfortunately, there really are no "clear instructions" for all graining on the cheap. It can certainly be done though, helps to be handy and a bit technically minded though.
Heatsticks economically apply heat to either pots or cooler tuns but be careful and knowledgeable w/ current!
The broke college way should also probably include a corona mill so you can reap the benefits of buying grain by the sack...few bucks upfront, but priced right grain is the only to brew cost effectively IMO!