My baby cousin is really stubborn, as in he doesn't listen to his mum when she tells him not to touch something, I have told her that he is too young and probably does not understand but she has resulted to hitting him on the hand and even this is not working... is there any way she can get this child to listen or is he just too young to undertand? He was born premature so I don't know if that has something to do with it or not?

Honestly this might sound harsh but it could be the parenting. When she tells him no and he keeps doing it does she keep saying no or does she eventually give up and let him do it anyway? What I have found works is simple ignoring. When the kid is doing something bad don't let him know your watching him don't touch him don't talk to him. Then when he is doing something good and listening or even just playing with his toys reward him with praise and maybe even a treat. However if you do give him a treat and you need to call it a treat. Like if you use call it a treat when he's beong rewarded and call it candy any other time. Also taking something away like his favorite toy or letting him go outside if he likes to do that works in harder situations. At first he will cry and it will be hard but his training her and you needs to be reversed into you raising him

This child sounds pretty typical to me. My son is nearly 3 now, and still "tests" the boundaries, touching, grabbing, that sort of thing. I don't think a lot of children really grow out of that for years to come... though it does get better. What I found to work the best for me and my son, is to get down on his level, and distract him with something else, that he likes to do, that is acceptable. For a lot of children, this will work, but only the mother/father and child will be able to make it work. Most, but not all the time, my son is receptive to this. If I am not doing something that can't be put down temporarily, I will even get down and play with him to help distract him from such things that I don't want him messing with.
As for her "hitting" the child, I can't say that this is a bad or good thing. Hitting isn't the best way of doing things, but it's not the worst, either. A lot of times, yelling can do more damage than a smack on the butt or hand. As long as she isn't "beating" the child, I wouldn't worry too much, just maybe suggest the "interuption" idea I presented here. It might be something she hasn't thought of that could work very well for her.
Good luck to you and your cousin.

LOL, my term for this is "octopus arms." They reach for everything and anything. It's quite normal and a developmental milestone.

I disagree with the above statement about ignoring. They need to learn their boundaries, but the parent must also remain consistent. Never ignore bad behavior.

Yes, very normal and it will get a lot worse over the next couple years. Then it gets better till they are about 15 and from 15 to 18 they don't listen at all any more.