It sounds less like aggression and more like a mixture of hormones/fear/him attempting to protect his only safe place (the cage). Even the bird who's bonded to me won't let me put my hand in her cage without attacking me. I need to get her out of the room in order to safely change her food and water without stressing her out.
Pet store birds often have horrible experiences with people (being grabbed and manhandled, having people poke the glass to get a reaction, ect). You gotta work slow with your hands. Put them near his cage while talking softly- not in a threatening way, mind you. Just have them there and work on gradually bringing them closer over time. Listen to him when he hisses- that's him giving you a warning before he flat-out bites you. They will often give you a warning before attacking like that.
What worked with my tiel was just sitting by her cage and allowing her to grow accustomed to me. I left the door open, talked sweetly to her, let her watch me as I did stuff on the computer. Eventually, she realized I wasn't scary and could be trusted to handle her.
Hand-offering treats should be done gradually. If he doesn't trust your hand or will bite you, try using a long spoon or a fork.
As far as vegetables go, I have a hard time with mine. What worked was coating vegetables in seeds and essentially tricking the bird into eating them. Dangling wet spinach leaves from the top of the cage is also an option.
If this is a hormonal issue, you can try putting him to bed earlier. Cockatiels need about 10 hours of total darkness. It might not help entirely, since he's a birdie teenager, but it might help make him a little less grouchy.
Just remember that all birds will bite, no matter how much they love you or how comfortable they feel with you. It's just a part of what makes a bird a bird.