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Your assumptions are all right.

Place of Birth: "Germania" is sufficient.

Residente in: this is where you live most of the year. Therefore, my suggestion is to write "Stati Uniti" and then, just next to it, making it fit in the tight space "Domiciliata in Siracua, Via V. Veneto n. [street number]". This is because, as indicated in the few lines under which you are about to sign, you are "criminally liable for false statements" and it would be wrong to state that you are resident in Italy, since you live in the US.

"n." is the street number (stands for "numero")

"cap" for siracusa is 96100 (http://www.poste.it/online/cercacap/elenco_locvie.php lists all italian postal codes)

"recapito telefonico" is a phone number (you can put the one of the people hosting you).

Ciao!