You ask about using 'faithfully' and 'sincerely' if you know someone; by this I take it you're asking about using those modes of address in formal or business correspondence (in personal correspondence, anything goes, literally!)
Generally, the exact mode of address depends on the relationship between the sender and the recipient. Sounds obvious doesn't it, but it really pays to keep that in mind.
Informal modes of address change frequently, but informality in business can only go so far.
A business letter where you know the recipient is now quite likely to begin Dear Alan and end Best wishes, Kind regards, or the slightly more formal Yours sincerely
To an anonymous person in a corporate entity the strictly correct Dear Sir(s) and Yours faithfully are better; at least, you will not be criticised for using those terms.
One other point about business letters - If you include a person's name in the address box at the top of the letter, then begin your letter Dear Mr Jones... or Dear Ms Smith....
Whether you finish with Yours sincerely or the more formal Yours faithfully is up to you.
I typically use "Kind Regards" or even more simply "Best" for someone I know.