Oddly enough, I've been unable to find anything when searching for proper horn use on the LIRR, specifically the route we have in TSW. I was hoping someone local or familiar with prototypical operations on the route can give me a hand. From what I gather they used to be required to sound the horns approaching stations but are no longer required to do so? What about for crossing? I don't see any whistle posts, does this basically just mean they are quiet crossings? Are all the crossings quiet? Thank you
No idea if this is still in force, it's quite old: https://www.everycrsreport.com/reports/RL33286.html
When approaching passenger stations, they are only required to sound the horn in short successions if they are not scheduled to stop at the station and they are approaching on tracks next to platforms when persons are not clear of the yellow safety line on the platform. This doesn't apply to Jamaica. The LIRR has standard whistle posts at all public highway grade crossings for which Rule 14L must be sounded, DTG just didn't bother to place them in the route for some strange, unknown reason. There are exceptions to this, mostly from a special instruction that allows the engineer to blow one short blast of the horn instead of 14L if the train is stopped at a station where there's a grade crossing right after the platform and the crossing gates are already down. There are blue diamond signs that read "S.I. 1103-G" for special instruction 1103-G where this exception applies. These wayside signs are also not in the route. DTG also There is also a quiet zone, or quiet crossing as you had mentioned. Engineers only sound 14L at a quiet zone crossing in an emergency situation such as a car on the tracks or the crossing gates malfunctioning. Quiet zones are indicated by a standard whistle post with a blue square sign above it with the letters "QZ". There's only one quiet zone on the entire railroad and that is Little Neck Parkway on the Port Washington branch, so it would'nt be in the route anyway. 
Yeah, such a shame for the missing whistle posts alongside the route. Level crossings aside, I believe they have many whistle post around bridges and underpasses as well. Also, I believe you are supposed to sound the horn twice before departing from Jamaica.
They have some whistle posts near tunnels and underpasses, mostly around Jamaica and the East River Tunnels. There is currently no rule or special instruction that requires sounding the horn prior to every departure at Jamaica, however there may have been one in the past back when Hall and Jay towers were open, although I can't be certain. Other reasons why you may hear the horn near Jamaica are to alert employees on or about the tracks traveling to and from various yards in the area or trains making reverse movements into yards. There are also whistle posts when entering the Atlantic Branch underpasses both east and west of the station.
I would love to see the entire system on TSW3, however I'm most interested in DTG adding the element of diesel operations along the route. I think the Oyster Bay branch would be most practical, considering Oyster Bay branch trains utilize the Mainline between Nassau interlocking and Long Island City, which is already part of the existing route. It would add much needed services to the underutilized Long Island City terminal and the route has several unique elements that would make it an interesting addition. To start, it is one of the most scenic branches in the system, traversing the hills of North Shore L.I. It'd also provide a good challenge, being that is has some of the steepest grades in the system and all short platforms that have a capacity of 4 cars (except Glen St). It is one of only two branches east of Jamaica to feature wayside automatic block signals, as well as a manual block signal system, with Rule 251 wayside automatic block signals between Nassau and Locust, and Rule 261 manual block signal system rules between Locust and End of Block Oyster Bay. Adding diesel to the route could also introduce new scenarios featuring Jamaica Storage Yard and Morris Park, with it's round table.
