They are both correct but their meanings are slightly different. The first line implies that we should be careful because of his youth. The second line implies that his youth is not a disadvantage when it comes to his computing ability. The first line would be better written as one sentence, with a comma after "however".

The second one is correct. It is similar with" Despite the fact that he is still young,he is good at computing." He gave me a bouquet of tulips yesterday.However,I won't forgive him.-(It doesn't matter what he does for me ,i won't forgive him).-an example with however I hope it makes sense.

The first one's better although both are correct. It will depend on the context you're using the sentence in.