Sorry I came to this question late. $F_q$ is undecidable from a presentation for each fixed $3\leq q<\infty$. First note that for finitely presented groups $F_q$ is equivalent to the homological finiteness condition $FP_q$ so it is enough to show this condition undecidable. This was done for $q =3$ in Section 5 of Cremanns, Robert; Otto, Friedrich, For groups the property of having finite derivation type is equivalent to the homological finiteness condition FP3. J. Symbolic Comput. 22 (1996), no. 2, 155–177. The same construction works for any fixed finite $q\geq 3$. They use essentially the same construction as the proof that Markov properties are undecidable but different details.

Sorry I came to this question late. $F_q$ is undecidable from a presentation for each fixed $3\leq q<\infty$. First note that for finitely presented groups $F_q$ is equivalent to the homological finiteness condition $FP_q$ so it is enough to show this condition undecidable. This was done for $q =3$ in Section 5 of Cremanns, Robert; Otto, Friedrich, For groups the property of having finite derivation type is equivalent to the homological finiteness condition FP3. J. Symbolic Comput. 22 (1996), no. 2, 155–177 https://www.sciencedirect.com/science/article/pii/S0747717196900462. The same construction works for any fixed finite $q\geq 3$. They use essentially the same construction as the proof that Markov properties are undecidable but different details.