Can all regular tree types be expressed as $\mu$ types?
You can reduce mutual recursion to a single recursion, see Bekic's Theorem, see e.g. Section 10.1 of Winskel's (1), where Bekic is worked out for programs rather than types. Note however that the details depend on the exact nature of the formal system in question. See A. Bauer's answer in (2) for the case of types.




G. Winskel, The Formal Semantics of Programming Languages.
CSTheory Stackexchange, Can Isorecursive types capture mutually recursive data types?