Hi,
Your understanding is mostly fine.
# 2 is a poor construction. In your construction, the man is drinking tea not Jack. There should be no comma. 'Drinking tea' is a participle phrase which you intended to describe Jack, I think. If I'm right, then the participle phrase needs to go as close to Jack as you can get it. If you wanted Jack to drink the tea, the sentence should be this: Jack, drinking tea, walked to the man. Or, Drinking tea, Jack walked to the man. If you wanted the man to rink the tea, remove the comma.
#3 is a poor construction. Drinking is a participle adjective. But in English, adjectives come before the noun they describe not after. Compare #3 to Jack drove up the winding road, not road winding. Jack teased the sleeping dog, not dog sleeping.
Cheers