Q: Car started to smoke a lot while driving

So my car started having problems when we noticed the water wasn’t being pumped due to air, so we wanted to buy a new radiator but never had the chance. Then about 2 months ago we bought new head gaskets, then about 5 days ago, we noticed the turbo start sounding weird, like it didn’t take in the air right, and also every time we accelerated, a noticeable amount of white/gray smoke would come out, but to my dad it looked black. Also had oil in the muffler. Then when he took the car to test it again, a lot of smoke came out of the hood of the car, he said the street was getting filled with smoke. And we don’t know if what exactly happened, if the messed up turbo caused it, or overheated due to need of new radiator. I really like the car but he thinks we won’t be able to fix it. I wanted to see what to do to fix it and keep it. Or atleast what you think are the problems.
My car has a manual transmission.