There's a friendly interaction to "Ask About Age"—the other sim will reply with a dialog box that says something like, "Sure, let's compare ages. It looks like I'm x days older/younger than you." Of course, you have to check your own sim's age for the comparison to help.
As @JoAnne65 said, NRaas MasterController shows sims' ages on the lists it generates when you're looking to run a command.
Even if you don't have MC, you can tell what age category whole groups of sims are in, as long as someone in your household already knows them: On the party invitation list, it shows the age group of any potential invitee. You can of course close the window once you see the list.
For the "Ask to Move In" function to show up, you need to be at least "good friends" (or close), and the other sim has to think yours is being "sociable" or "friendly" in the conversation. The interaction is also under the Friendly category. Plus, you can't have more than eight sims in your current household, including any pregnancies, unless you have NRaas Mover in place.