major issues, nothin but headaches seized motor??

I am really having some issues with this car i recently bought

I foguht through a draw and found it was the alternator, then the car wouldnt crank, just solenoid buzz, so i charged up a battery and put it in there went to start it and smoke came out the cowl hood, it was coming from the back of the engine down below

I was lookin at some stuff and found that the antifreeze was pretty low in the fill tank, there was some in the radiator but basically none in the tank

I didnt try to crank it manually with a wrench on the crankshaft pulley couldnt get at it, I just pulled the car to a shop cuz im sick of dealing with the problems

anyone have any idea whats my issue here, cuz i dont have a clue

well what do you need to know?

i just been real frustrated with this thing
i thought it mgiht be a seized starter or maybe it was hung up, but never hit it or anything

it ran fine until i parked it like a week then it wouldnt started and solenoid made a rat-tat-tat-tat sound, then i been dealin with that ever since, put a fully charged battery in cranked it once and seen smoke, solenoid didnt make a noise this time

pretty sure when i put the wires on solenoid they were right i put them in same locations im pretty sure, and it was causing troubles with the rat tat tating before the solenoid was replaced

solenoid was my first thought