번역 - 독일어-이탈리아어 - Ich wünsche dir einen schönen Tag. ...

Hi Aneta!

Your translation is grammatically and lexically correct, but it would sound a bit weird to a native speaker.

First, the last option you gave in the remarks field (i.e. buona giornata) is the most used and the one I'd recommend, but has no verb and thus breaks our rule #4.
The main translation you gave would be the 2nd most heard, so it's OK if you make those two little edits:

1. "abbia" -> "abbi"
The former is 3rd person, while the latter is 2nd person. It's true English doesn't make such distinctions, but the source text is in German and "dir" is a 2nd singular person.

2. "un giorno piacevole " -> "una giornata piacevole"
GIORNATA can always be replaced with GIORNO except when you talk about work (i.e. "workday" is "giornata lavorativa" and "day off" is "giornata di riposo" ) and when you talk to someone who's leaving (i.e. "have a good day" is "buona giornata" ).

Finally, "Amore e baci" is not very used at the end of letters and email. I searched something about the German expression "Alles liebe", and it seems it is kind of equivalent to Italian Con affetto.

Do you agree?

Of course I agree!
Thank you so much for your corrections, dear Alex. It's good to learn the natural Italian expressions. I realize my Italian is still very stiff and academic.

Your Italian is actually excellent, Aneta!
But it's also true that you need to speak with native speakers to learn such things.

E vero! Allora dimmi più spesso, per favore.

Con piacere!

I meant: parla con me!

I was waiting for your correction indeed