An equivalent for "it'll be done" can be "dalo por hecho" or "cuenta con eso" ("you can count on that"). Other possibilities are "así será" or "así se hará", but these show a clear hierarchy. Depending on the context, we might just say "no te preocupes". I had never given it too much thought, but I would say we don't use the verb that way a lot ("be done") in short answers.
It's possible to say "ni lo menciones", but it's not too common. Shorter and more frequent equivalent are "de nada" (standard; plain "you're welcome"), "no es nada" or "no hay de qué" (somewhat informal).
The rest are: please: por favor thank you: gracias I'm sorry: lo siento/ lo lamento/ perdón (stronger) congratulations: felicidades thank heavens: gracias al cielo nonsense: tonterías
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