‘nel piatto [fondo]’ means “in the [deep] plate”.

‘sul piatto [piano]’ means “on the [flat] plate”.

I think "nel piatto" translates to "in the plate", and "sul piatto" translates to "on the plate".

I'm not a native or fluent speaker , so i may be wrong. But i think "nel" is something like a contraction for "in the..." As it can be nel, nello, negli, etc. as would be the definite article it is replacing.

Yes

lo is only used when a masculine noun begins with a "z" or "s plus a consonant" so with piatto it is nel

Also, nel is a combination of the Italian word "in" and a definite article. So I don't believe you would combine nel with another definite article.

'nel' is a combination of 'in' + 'il', while 'nello' is a combination of 'in' + 'lo'. Basically two different articles in the second part. 'Lo' is used before masculine words that start with 'z', or 's' + consonant. 'Il' is used before masculine words that start with any other consonant.

The definite article almost always precedes the possessive word (except in cases when referring to singular family members, such as "mia madre").

Nostra -> feminine, nostro -> masculine.

Torta is feminine, it's comply with nostra.

Il piatto not lo piatto. (The correct article for piatto is il)

Nello = in+lo. Nel =in+il.

Only one cake: lA tortA nostrA

-a is feminine, -o is masculine (referring to the thing that 'we' own)

Differences in gender and number. -o = masculine singular, -a = feminine singular, -i = masculine plural, -e = feminine plural