Is there anything reported from the Prophet (peace be upon him) that prohibits or dislikes specific hairstyles such as "spiky," "waxed," and "dax"?

There is no specific Sunnah concerning men's hairstyling, nor is any particular style disliked. However, the Prophet, peace and blessings be upon him, forbade Al-Qaza' (shaving parts of the head and leaving others), the imitation of women by men and men by women, and the imitation of disbelievers.

Therefore, there is no harm in styling the hair in any way that adorns it, provided it does not involve imitating disbelievers or transgressors, or men imitating women, or vice versa.