So many different questions..... First off, I recommend you visiting
https://en.wikipedia.org/wiki/New_York_City_Fire_Department_Bureau_of_EMS , which explains a little bit. Then feel free to check out
https://emtlife.com/threads/ems-in-new-york-city.21301/
To answer your questions one by one:
How does the New York ambulance system works exactly?
poorly? It's a system that is called one of the best in the nation by those who work in it, which is an opinion shared by no one who works outside of it.
I see there are multiple ambulance providers on the streets (SeniorCare, FDNY, New York Presbyterian, some volunteers, AMR, etc).
you are correct; FDNY EMS has 2/3 of the ambulances within the FDNY EMS system; the remaining 1/3 are voluntary ambulances that are run by either the hospitals or private companies within NYC. They operate on a "closest ambulance" dispatch system, and in theory, all ambulances have the same capabilities.
Are the ambulances always stationed at specific locations in the city for 911 calls when not on a call?
Almost all the FDNY EMS units are posted on street corners throughout the city. some of the hospital based units are located in stations.
Or does the FDNY dispatcher let the ambulances (from all different providers) station randomly in the city?
no, each unit is assigned a particular area, IIRC, a 4 block area where they are supposed to post. hospital based units are typically located near their base hospitals.
And is the garage for service/maintenance and parking off-duty ambulances only, or do they also respond out of those garages?
as mentioned before, the vast majority of ambulances are posted on street corners. there are several "stations" where off duty ambulances are parked, but once a crew signs on duty, they are expected to leave the station and go to their street corner.
Are the 911 ambulances also used for interclinical transports? Or are those services strictly seperated from 911 ambulances and assigned to special teams?
To my knowledge, FDNY doesn't do interfacility transports, between hospitals.
To answer some more questions that weren't asked: FDNY EMS
is the busiest EMS system in the US, in terms of overall call volume; however their number of calls per truck is no where near the highest, especially among urban EMS systems. FDNY EMS works 8 hour shifts; from what my former colleagues told me, typically call volume is 4 calls per shift... at 6, they consider themselves to be slammed. The majority of FDNY EMS employees are working EMS until they can (hopefully) "promote" to the suppression side.
There are "volunteer" EMS agencies (meaning, members of the organization who don't get paid to be on the ambulance) that operate in NYC;
https://www.cpmu.com/ ,
https://en.wikipedia.org/wiki/Bedford-Stuyvesant_Volunteer_Ambulance_Corps and
https://hatzalah.org/twotiered.php,
http://lindenwoodvac.org/,
http://www.glencoveems.com/ ,
http://www.fhvac.org/ all operate within NYC, but technically outside the FDNY EMS system. They have a self assigned coverage area, and will usually jump a call that they hear on the scanner, or will answer calls that are called into their dispatch center instead of go to 911. When the 911 system truck arrives, they just advise dispatch that an ambulance is on scene with patient care, and they go available.
TL
R it's a huge mess.