You use "like" to show that two things are the same, and "dislike" to show that they are different.
He is not fond of sweets, like his brother.
He is not fond of sweets. His brother is like him. His brother is the same as him. His brother also does not like sweets.
This is NOT the meaning you want.
He is not fond of sweets, unlike his brother.
He is not fond of sweets. His brother is NOT like him. His brother is different than him. His brother DOES like sweets.
This is the meaning you want.
As for your last question, removing the comma does change the meaning.
He is not fond of sweets like his brother.
This sentence doesn't make sense in the real world. It is suggesting that his brother IS a sweet, and that he doesn't like his brother. With the comma, the speaker is not fond of sweets. Without the comma, the speaker is not fond of sweets like his brother.
For this sentence to be correct, the brother would have to be made out of chocolate. The subject may or may not like sweets in general, but he does not like his chocolate-brother.
Some more ambiguous meanings could be interpreted as well when comma is left out, as pointed out in the answer by ColleenV