The first sentence should be 馬克説得比我好一些 and it means "Mark speaks Chinese a bit better than I do". 一些 just means "some", although if pushed I'd say 一些 is slightly more than 一點.
我的漢語沒有他好, or, 我的漢語沒有他的好 means "My Chinese isn't as good as his". Here, A沒有B+adj. is saying "B is (more) adj. than A"
我的房子沒有他的大 My house isn't as big as his
瑪麗沒有馬克高 Mary isn't as tall as Mark