Disclaimer: I'm no expert, but here's an answer as I understand these states.
1. Can massless bosonic particles such as photons, magnons, phonons, etc. with zero chemical potential Bose condense?
The short answer is no, they cannot. A BEC is characterized by an extensive population of the groundstate, and is in a confined region. Massless particles described by the Bose-Einstein distribution with $\mu=0$ will always have a vanishing occupation of the groundstate ($E\rightarrow 0$). See the answers to Why zero chemical potential does not allow the Bose-Einstein Condensation of Phonons? for more details.
2. Can particles such as photons, magnons, phonons, etc. Bose condense?
Yes, they can, just as the answers to the question Can a system entirely of photons be a Bose-Einsten condensate? suggest for photons. For completeness, here are some relevant experimental references:
3. Do we have a theoretical problem?
Points 1. and 2. are seemingly in disagreement, so perhaps we have. However, the $\mu=0$ condition is derived in equilibrium. By working away from equilibrium, the requirement is sidestepped. In particular, one can engineer a quasi-equilibrium with conserved particle number - and hence non-zero chemical potential, making Bose condensation possible. This relies on a balance of lifetimes of the particles and the rate at which new particles are pumped into the system, which is a technical challenge but demonstrably possible.