"The pasta on the plate is his."
Translation:La pasta nel piatto è la sua.
Are you reading the lessons, clickable from the light bulb on the individual lesson plan, before doing the exercises? They give a whole page of instructions for how to use each lesson. For this one, it says:
Italian possessives are in the form definite article (il, la, i, le) + possessive adjective. They agree with the gender and number of the thing they describe:
My/Mine: "il mio", "la mia", "i miei", "le mie" Your/Yours (sing): "il tuo", "la tua", "i tuoi", "le tue" His/Hers/Its/Your (formal)/Yours (formal): "il suo", "la sua", "i suoi", "le sue" Our/Ours: "il nostro", "la nostra", "i nostri", "le nostre" Your/Yours (plur): "il vostro", "la vostra", "i vostri", "le vostre" Their/Theirs: "il loro", "la loro", "i loro", "le loro" il mio cane My dog ("Cane" is masculine singular, so we use "il" and "mio.")
la mia pizza My pizza ("Pizza" is feminine singular, so we use "la" and "mia.")
Even though in English the possessive in the third person (his, her, its) varies based on the owner, remember that in Italian the gender and number are determined by the thing being owned:
il cane di Giulia > il suo cane ("Cane" is masculine, so we use the masculine, even though it is her dog.)
In Italian an article is almost always mandatory before a possessive. The exceptions are:
It's not used before close family members, in the singular and not modified, e.g. "mio padre" (my father), unless the possessive is "loro" (in which case the article is needed). It's optional when the possessive adjective is alone following a form of "essere," e.g. "è mio" (it's mine). It's not used in a small number of set phrases, e.g. "casa mia" (my home). Possessive pronouns (possessives acting as a noun) are formed using the definite article and the possessive. They agree with the object they describe, even if it is not explicitly mentioned in the sentence:
Dov'è la tua macchina? La mia è qui. Where is your car? Mine is here. (It is understood that "la mia" refers to my car, so it is feminine.)
These are possessive adjectives so they describe who possesses a noun and they behave like other adjectives. Like other adjectives the endings change with the gender and number of the noun being described. So, "il suo" is for a masculine singular noun, "la sua" is for a feminine singular noun, "i suoi" is masculine plural and "le sue" is feminine plural. They all mean "his," "hers" or "its" (In formal speech they can also mean "your.") Hence the answer to your last question is no.
You can't say "nel piatto", but "sul piatto" referring to "on the plate" ...