From discussing it with my local signallers (in person), it appears they would prefer as much of an obvious description of the location as possible. You don't even have to use especially technical terminology (eg. "the line through Purley Oaks Platform 2" will suffice as a good description to relay, firstly). Anything that can be clearly relayed is better than nothing, provided it is accurate. Remember that there will be a "lead" person in the conversation who should be able to request and sort out any clarification, if it is required. Use a fixed telephone if you can. Look for the green emergency phone symbol (many stations, platform ramps and other places have emergency phones - way more than you'd expect if you weren't familiar with them), a signal post telephone, a level crossing telephone, or just the "black on white" phone symbol on a cupboard (a standard telephone for railway use).
Bridge numbers, identification plates etc. are all very useful (and I mean that sincerely) if you have time to search for the details and get them to hand before taking action, but sometimes these things can, with the best of intentions, be less handy than a more colloquial description. Unless you have a bridge or other plate specifically advising that any incident should be treated as prescribed and by giving a specific reference, it would perhaps be best to just detail the location's defining features (and not "not where they are", as in, "I have just left Hassocks and have absolutely no idea where we are, but we're near a sort of stream"). You can mention the plate as an immediate secondary identifier. I am tailoring this to the public and not to railway staff - obviously any on here will know the protocols if they are competent! There are two risks - firstly that someone will spend too much time looking up a small piece of information which may be redundant, linked to an unrelated feature or may not link to the required location information, and secondly that the plate or other identifying mark may just be something like an unusual car stop marker, which would probably not be very helpful at all. The only exception I'd give would be a plate affixed to the signal such as "VC191", which details the signal number.
As for a poor response to issues such as open gates, stating hazards and positive actions required (eg. "this gate needs a new padlock because it is currently open to lots of nearby schoolchildren") is a good way to go about it. I wouldn't suggest for a moment that you either exaggerated or didn't send the right message, as call takers can of course vary just with anyone in any other job, but emphasising the issue and what could be done about it (don't worry - when qualified professionals turn up, if your suggestion isn't safe, then no unsafe work should be done as a result - it just builds a picture) is the right way forward.
I think much of what needs to be said about calling the emergency services has been said. The operator and the call handler should be able to prioritise and arrange for someone to dispatch resources and supervisors should pick up on when a major incident is kicking off. I say "should", as I am sure there are times it does not happen, but in my experience there are not too many incidents of a major nature where the phone call has clarity and it is not ascertained by the call handlers / their management that something major is ongoing.
As with all safety-critical communications, speak from somewhere safe (not in the middle of a fuel spill or fire!), speak a touch slower than you would normally (if you are stressed, this may turn out to be a speed that's "just right"), shield yourself from the wind (no use if you can't be heard!), and follow any prompts, repeating information as needed until you can be sure it is understood clearly. The message is vital, and if it is being received by trained call handlers in a dedicated emergency facility, will go to the right place.