What engine and 4WD system do you have?
The 1st Pic, it looks like the heater hoses have been cut. You should NOT have gotten any heat out of the environmental system, if you did get a tiny bit of heat, it might have been heat from the engine compartment warming parts inside the environmental control system of the engine enough to create a bit of heat.
Since there are "T"'s in the heater hoses, you probably have a rear heat/ac system. Whomever cut the heater hoses, must have put a loop on the source at the engine (i.e. looped the output to the return) otherwise you would have squirted out all your coolant within minutes and the engine would be overheating. Check the output & return of the heater hoses, on the 3.7L V6 (and likely the 4.7 V8, since they are very similar engines) there are 2 nipples by the lower radiator hose on the engine. Likely you will find a hose in a half loop connecting the two, or someone removed the nipples and replaced them with plugs.
Sadly the only reason someone would do this is because one of the heater cores is leaking and they did NOT want to spend the money/time to fix it. It's possible that just one of the hoses was leaking, but you'd have to be pretty darn lazy to cut all the hoses just to avoid replacing a single hose. But lets hope that was the case, otherwise you need to replace the heater core, DIY is very difficult and takes a long time, you have to pull the dash, paying a shop to do it is very expensive because of all the labor involved.
One option to consider, is too bring the vehicle back to the seller and insist on return and refund or they repair the vehicle, because those cut heater hoses didn't happen by accident or part of normal wear and tear, it was done intentionally, likely to keep the vehicle operating without repairing it properly. The owner would know about it, a dealer selling it should have caught it in an inspection. They knowingly sold you a vehicle that needed a very expensive repair and didn't tell you about it during the sale.
If you want to repair this yourself, you need to replace the cut heater hoses and then see if you experience leaking heater cores, and replace the heater cores that leak at that point, if they do.
You can just get basic heater hose is you want, and replace the cut lines, get a "T" from the plumbing section of a hardware store. Or you can purchase replacement lines from the dealer that are preformed with the "T" built in. You can just forget the "T"s and run it to the front heater core.
Make sure you use the correct anti-freeze, HOAT, either get if from the dealer or use Zerex G-05, a lot of other anti-freezes claim to mix with anything is a totally bogus claim, they are the wrong anti-freeze and they do NOT mix any anti-freeze, in fact if the previous owner used one of those B.S. anti-freezes from Prestone or others, that might have caused the problems you have now.