If all the strings buzzed at the 1st fret that is a sure sign that the truss rod has been overtightened. Some players do this to achieve a very straight neck with super-low action. But if overtightened the headstock is pushed downward, your neck is shaped like a frown. :(
This will cause fret buzz usually between frets 1-5. The opposite is too much "relief" where the neck is upbowed like a smile. This will usually cause fretbuzz between frets 5-12. When you fret a string at these frets they touch a fret higher up the fretboard.
A truss rod adjustment is very easy to perform and should not cost much. Still, someone who advertises a guitar as professional setup should have caught this. And it is hard to believe the other defects would not have been spotted. It does sound like this seller purposely misrepresented this guitar.
Contact the seller, see if you can get a little refund, I did that once and got $50 off the price. Should pay for the setup. If the seller is uncooperative, leave negative feedback. But be polite about your comments. If you say "this seller is a &#^$%@&@!!!" people will take his side. If you politely state the problems people will take your side.
Good luck.
If you know something better than Rock and Roll, I'd like to hear it - Jerry Lee Lewis
