Can a Turing Machine decide only non-regular languages?
@Karolis Juodele already gave the answer, and your answer is also correct.

Another thing to keep in mind is although infinite languages can be undecidable, some of them are regular.. ex. $\{0\}^* \subset \{0,1\}^*$ is an infinite language but is regular (you can construct a FSM, with a single state, that accepts it).

Basically any undecidable language is infinite, but any infinite language is not necessarily undecidable.

Also, for a language like $L = \{w \mid m \text{ halts on the input } w\}$, there exists a Turing Machine for which $L$ is undecidable.