Actually, enthalpy H is defined as the internal energy U plus the product PV where U, P, and V are state functions... my brain is dead.
Yes, q is just a way of keeping track of heat. Just as a bank account has positive and negative numbers at times for when you owe and when you have money. Yes and whether or not delta H is positive or negative can also tell you whether or not the reaction requires energy to start or gives energy out.
You do calorimetry, measurement of heat, with a calorimeter, a device used to measure heat.
A coffee-cup calorimeter is a poor-man's bomb calorimeter. A bomb calorimeter basically is filled up with 6ATM of oxygen with an iron filament that is covered with a compound of interest. A huge voltage is put across the filament and in the presence of oxygen burns everything including the compound. The pressure created from this bomb, in a well designed bomb calorimeter, actually puts pressure to keep its lid on tighter. This whole thing is kept in a big tank of circulating water to keep track of heat, which is put in another container to keep stray heat from coming in or leaving the device.
A coffee-cup calorimeter is just two coffee-cups that seperate the environment from the reaction happening in the cup and involves no explosions. Actually, the insulating power of the cups is very very good.