From my understanding there are 4 different types of deicing fluids.
I am building software for a school project and with the software I want to determine if deicing is needed for a flight.
I'm mainly addressing your "with the software I want to determine if deicing is needed for a flight."
There are three possibilities for whether deicing is needed or not, which are based primarily on actual and expected weather conditions (both at the point of departure, enroute, and possibly at the destination) and the airplane's capabilities:
No reasonable pilot is going to request deicing in a case where deicing is obviously not required, so that leaves us with the other two. (Remember that deicing costs the airline money, and a pilot who regularly requests deicing for a short local hop in the height of summer is probably going to get talked to by their boss about it.)
If deicing might be required, it's basically at pilot's discretion, likely supported by company standard operating procedures and airplane manufacturer recommendations.
If deicing is obviously required, any pilot who does not request (and wait for) deicing before beginning the takeoff roll is delinquient in their duties, and is putting both the passengers, the crew, and the airframe at risk. Unfortunately, there have been crashes where a decision to not deice in conditions that required deicing were a major contributing factor.
Thus, if deicing is determined to be needed, yet not requested and waited for, then the only safe alternative remaining is to stay on the ground; effectively cancelling the flight.
Consequently, the options are:
If it is known while the aircraft is still on the ground that a flight cannot be done safely, then the flight should be cancelled.
A flight cancellation can, simplistically, be modeled as an infinite delay.
Therefore, we can conclude that if deicing is needed, then waiting for deicing is required, and whatever this means in terms of additional delay will simply have to be tolerated as a necessity for the ability to safely undertake the flight. It's really not different from inoperative critical flight instruments; if, for example, all attitude indicators or airspeed indicators disagree, you're just going to have to wait to get that fixed, too.
In an ideal world, the choice of whether or not to deice the airplane is entirely unrelated to the time required to deice the airplane.
Trying to answer questions 1 through 3 here. Pilots have two main parameters to think about when deciding what type of fluid to use when de-icing: turnaround time and speed of the aircraft when flying.
Type I has a low viscosity so will usually be used when the aircraft will be leaving soon as it also doesn't protect it for very long, but is useful for slower aircraft has it will also easily flow off the surface.
Type II is more viscous and will, therefore, stay on the aircraft until a higher speed but will also protect it from ice for a longer period of time.
Type III is a compromise between the two, allowing slower aircrafts longer time between de-icing and flight.
Type IV is essentially the same as Type II but with an even longer protection while not in flight.
In terms of holdover differences, as far as I am aware, there isn't any. Each type of fluid is spread on the surfaces from a hose, connected to the reservoir of the de-icing truck, meaning the actual application of the fluid is the same for all types.
From what I know, whenever the pilot calls for de-icing, the choice of type is made when the truck arrives, and the de-icer just selects that types and applies it. Therefore, there is no need to wait for a specific fluid-carrying truck to be available. Some airports even have trucks positioned in specific places on the taxiway and each aircraft taxies through that point to get de-iced before taking off (see below) Again, when the plane arrives at the position, it "orders" the fluid, and it is applied right away.
I don't have a source for this second part, I just used my own experience and observations.
