"Congratulations" and "best wishes" do not have the same meaning in English. The first is an expression of acknowledgement for something already achieved, and the latter is a desire for another's success in the future.
Not necessarily. You can use this phrase when saying goodbye to someone, like "i wish you the best"
I don't see it fitting in portugese.
And The most common moment to hear this is exactly in your birthday.
I received a notification from here now and how my birthday was yesterday i thought was a wish from duolingo to me when i saw the subject on my mailbox.
On the other hand, you could use:
Abraços, [your name] = (for someone familiar OR known);
Agradeço desde já, [your name] = (after you require something to someone);
*Atenciosamente, [your name] = (most common way to end a formal letter)
Felicidades (plural) = happinesses (plural). What the traduction "happinesses for you" is wrong? It is the literal traduction.
The plural is not used in English. We also would not say this without the verb "wishing". (Could also be I wish you or we wish you.) I feel like there might be other verbs that work but I can't think of any.
Things that use my can be used with sending, e.g. I'm sending my love, or I'm sending my best wishes.