How do I help my young kitten adjust?

I just got a male kitten last night from an owner who's 2 cats recently had kittens. When I went to pick him up she told me that he was 6-7wks old, eating hard food and using the litter pan! Once I got him home and really started observing him and l handling him I realized there is NO WAY he can be that old. He can't be over 3-4wks old! He will not eat hard food, can food or use the bathroom. I have since gone and picked up kitten milk from the store and fed that to him. He is drinking that fine, but about an hour after eating it he threw up then kept slobbering! I got him calmed back down and he is sleeping now! I also noticed when I got him home that his eyes had gunk in them! I have cleaned them up the way my VET suggested with warm water. I also had to bath him and pick the mounds of fleas off of him! I was just wondering if there was anything else I could do for this little guy! I am furious with the lady who gave him away too soon. She had him and 7 other kittens in a box ready to go. Their living conditions were very poor, so that's why I still took him. Not to mention his mom was long gone! Please help!