You might consider simply sincerely. Sincerely yours does sound a bit off to me for professional correspondence; I might indeed be sincere, but it's doubtful I'm theirs. Regards has always sounded a bit stiff to me, but I wouldn't look twice at it; it's common enough. Even sincerely sounds strange to me for email; I would certainly recommend it for a handwritten letter, though.
You've got to consider the difference in levels of formality between email and letters. For a letter, this would look perfectly fine to me:
Dear Jane,
[body of letter]
Sincerely,
[name]
But in an email we're generally much less formal, both in closing and opening. I'd take off the dear and use something less formal for the closing. For example:
Jane,
[body of email]
Thanks,
[name]
But plenty of people do use regards, and no one is going to think it strange if you do. Sometimes emails begin with hi as well. There's really nothing wrong with always using the same closing, either, so if regards works for you, use it! In fact I think most people do use the same closing most of the time. Considering my own email habits, I think I tend to do one of three things: 1) If I'm just sending along information, I don't use a closing at all; I simply end with my name. 2) If I'm requesting something of someone, or thanking them for something they've already done, I'll use thanks. 3) If I've written a significantly longer-than-usual email or am requesting significant effort on the recipient's part, I might end with thank you for your time. In a letter, I pretty much always use sincerely. In my experience, most people do. But email varies quite widely, so I wouldn't worry about this too much!
Nowadays, social protocols regarding forms of address in 'polite society' in western English-speaking countries are much more relaxed than they were 100 or 200 years ago, especially in the USA (and even in stuffy old Britain).
Unless you're part of the Hollywood crowd or a London West End actor, most people would probably reserve 'Darling' for people with whom they have a romantic relationship. 'Dear' also implies a certain degree of (at least emotional) intimacy.
But I don't think age differences are much of a factor now in terms of the general expectations that people have about how they ought to address one another.
The chief exception is perhaps such limited circumstances as where a large status difference is coupled with an occasion of some formality, especially when it also involves an official hierarchy with its associated rules of proper conduct (such as pertains to a branch of the armed forces).
Best Answer
Yes, long time no see is an appropriate phrase in the situation you described.
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