CL-650 Captain reported confusing ATC communication issues on arrival into MIA involving two aircraft with similar callsigns and apparent lack of clear communications from the Controller.

Narrative

On arrival to MIA; we experienced some seriously unprofessional service from Miami Approach. First; we were vectored into the wake turbulence of a heavy jet at about 17;000 ft.; and then; there was mass confusion between [another aircraft] and us. The Controller; even after acknowledging that there were two [aircraft with similar callsigns] on the frequency; continued to use the abbreviated call sign. There were numerous calls where; now; looking back; we can't be sure that we didn't take the other aircraft's clearances several times. There were some times where it was obvious; like when it would have been a 270º turn; and so we queried on it; to then find out it was meant for the other aircraft. There is really no way that we can know if we did or did not take the other aircraft's instructions; possibly more than once; unless a detailed review of the tapes and radar are done. I am 90% sure that my Co-Captain who was on the radios; read back the whole call sign each and every time.As on certain days; such as busy holiday weekends; there are ALWAYS multiple [similar] callsigns on the frequency; especially in South Florida; the FARs should be changed so that when there are more than one aircraft on a frequency with the same last two letters; the controller is REQUIRED to use the full callsign. Alternatively; for the sake of safety; we could find a way for the [air carrier] callsign could be used internationally. There has to be some way to get relief from whatever the tax ramifications are that are keeping us from being able to use the callsign internationally. There are many; many indicators out there that are screaming that the US Airspace System is heading for a major issue. Mistakes and lackadaisical compliance seems to be increasing everywhere. Everyone needs to tighten up on their attention to detail; and hold themselves to impeccable standards.