I don't think you can tackle all 3 simultaneously. Maybe if he was older then you could transition out of multiple bad habits althogether, but my gut says at age 2, you will need to tackle "stages".
He probably wants your hair because it means mama is close. Moving him to his own room/bed will knock out the hair and co-sleeping, although he will 1.) probably wake up crying in the middle of the night and 2.) might not stay in his bed (I should add that I'm biased about 2 year olds having the mental ability to understand the boundaries of a bed. I think kids need to be closer to age three to understand 'stay in bed'... that being said, you might need him to go to a crib following the initial weeks/months after the transition to his own room).
AND SUPER IMPORTANT: Once you start the transition to his own room, do not back down. Hold firm. He needs to learn that there are no other places for him to sleep.
Can you give him something else of "yours" to replace the hair...? Nothing too long and stringy that could pose a choking hazard though.
As for thumb sucking... Get him sleeping in his room, then tackle that. Thumb sucking is his comfort/soothing device. Taking away his "hair'" and putting him in his own room to sleep alone will be a big adjustment for him. If you don't let him suck his thumb, he'll probably redirect towards sucking clothes, bedding, stuffed animals... My 2 cents: let him suck his thumb to sleep. Work on ending that when he's 3-4.