How to find a sim's age?

If you have the Master Controller mod installed, you can click on the SIM in question and click "status". It'll tell you the age and any other information you want to know.

I don't know why you got the option for the dance, unless you have your teen settings on a short age span.

For example, I have my teens set at "18 days" to mimic 18 years. My oldest teen had her dance a few days ago (Real time) and now she's at Uni. Her siblings are in the middle (and one just starting) their teens and they haven't had the option yet.

If you click on City Hall and choose nraas>sim, for whatever option you pick, a list of sims will appear along with their ages and portraits. You'd have to do some math, but for example on an unaltered normal lifespan, teens' ages range from 17 (on the day they age up from child) to 31 (on their YA birthdays). You can also use sim>focus and then pick "by age" and select "teen" if you want to see the entire town's population, although this will exclude true NPCs (for teens, all of the babysitters) who are not working and therefore are probably nowhere at the moment.

MC has two options to change a sim's age, Age: Absolute and Age: Relative; I believe both are under sim>intermediate (or possibly basic instead). With Absolute, you can set the age of the sim in question to one day short of her birthday, if you want; before you change the number, it will display how many days she has been a child, so you can also use this function to see when she would age up naturally. You can also just use MC to "trigger age transition," under sim>intermediate, if you're getting antsy.

As far as SP, there are a ton of settings you could customize, like Disallow Romantic for certain sims, but you should ask the experts (of which I am not one). There might also be something you can do to adjust how much time passes before another formal dance. You can use MC to force a sim to quit a job, or even dissolve a romance, if you don't like it. sim>intermediate>career and sim>intermediate>long-term relationship: by category, respectively; the latter lets you choose a second sim and then which category you want to assign to their relationship, like good friends instead of bf/gf.

For proms: If you have the NRaas SP Careers module (not the NRaas Careers mod the SP Careers module) you might try:

City Hall or computer>NRaas>StoryProgression>General Options>Options: Situations>Options: Grads/Proms/Curfew>

Prom Chance Per Day>Default is 50%. Maybe change to 0. (This is the chance that the game will schedule a prom.)
Prom Cooldown>I think the default is 14 (in my game at university it's 33, but that might be because I'm playing on a longer lifespan). Maybe set this shorter.

When you are ready for a prom then go change the chance per day back to 50% or higher and shorten the cooldown.

If you want a sim to age up immediately click on the sim>NRaas>MasterController>Intermediate>Trigger Age Transition. I think that will work with inactives, but I don't think I've ever actually done so (I use that for actives all the time). I'd invite the inactive sim over to visit, then try that command (and exit without saving if anything goes wrong).

Sim>NRaas>Status>Personal should tell you a sim's age and days to transition.

edit: you can disallow teens from finding jobs with SP under the teenagers caste. I don't know if it's possible to delay them getting part time jobs though. Not sure how to slow down relationships forming other than slowing down SP's romance manager entirely. You're better off asking on the NRaas site.

NRaas Tagger will also tell you the age of all sims in town (and their relationship orientation) if you have it turned on for that (which I find incredibly helpful). I like to pair my sims with inactives that have ages within a couple of days of my sim.