Water pump and timing belt replaced now engine runs badly

I recently replaced the radiator, thermostat, thermostat housing, and lastly water pump and timing belt, ( water pump and timing belt was done at the mechanic). When I got my vehicle back from the mechanic it was running rough at startup and blowing white smoke until it warms up. I immediately called them and took it back in. They attempted for about thirty five minutes to get the engine to overheat but it would not. Fans came on and the temperature would go down. He told me to drive it that day and see if it overheats. I drove it for about thirty miles including sitting through two drive through's it never overheated. That next morning when I woke up the coolant had leaked out overnight from what looked to be the water pump. So I took it back to the mechanic. They pulled the water pump to fix it and did a pressure test and said the leak was coming from behind the timing casing/housing. The mechanic said his fear is replacing that and the real reason it is not holding pressure is because there is a blown head gasket. I asked him to put the water pump back on and fill with coolant and told him I would make a decision on what to do. At this point I pick up my car drive it home and want to get a second opinion to determine for sure if it is a head gasket. I wanted to think maybe it was a intake manifold gasket which is much cheaper to replace, This time when I pick it up the CEL is on and I stop by Autozone to get it read the codes that came up where:
P1684, P0562, P0152, P0352, P0133, P0325, and P0113, the last two codes repeated a few times each. I woke up this morning and I see the puddle of fluid at the bottom front side dripping from the radiator. I plan on going to get a second opinion but before I did I just thought I would ask if there is any chance of saving this vehicle? I would love to get it repaired but cannot afford to put a new engine in. Please advise what you think it may be and where to start. Also, just so you know when I got it from the shop the first time they informed me the alternator and o2 sensor needed to be replaced as well as a motor mount. I just wanted to throw that in there in case it was relevant to any of the codes that come up. Thanks for any input it is so much appreciated.

Also, forgot to mention there is no water or coolant in my oil, no oil in coolant.