First important fact about ZX-calculus: it is universal.
Theorem (informal, van de Wetering, 2020): Every complex matrix of size $2^n \times 2^m$ for some $n$ and $m$ can be represented in the ZX-calculus.
In particular, every map from qubits to qubits can be written as a ZX-diagram. Universality can be showed simply showing that a universal set of quantum gates have ZX-diagram representation.
Theorem (Coecke and Kissinger, 2018): Any $n$-qubit unitary can be constructed out of CNOT gates and phase gates.
For the second part, the $Y$-axis rotation can be written in terms of Z and X consecutive rotations together with a phase. Therefore a $Y$ gate can be written as,
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as was written (van de Wetering, 2020), see the cheatsheet A.2.
