Learn Italian: La sua idea ha senso, secondo me. - His idea makes sense, in my opinion.

Yes! In Italian, possessive adjectives like sua agree with the gender of the noun being owned (the feminine idea), not the gender of the person who owns it. Without extra context, la sua idea could mean 'his idea', 'her idea', or even the formal 'your idea'.

In English we say an idea 'makes' sense. Why does Italian use ha senso (has sense)?

Italian expresses this concept with the verb avere (to have). Be careful not to literally translate 'makes sense' as fa senso. In Italian, the idiom fare senso actually means to be disgusting or to make someone feel sick!

Can I say nella mia opinione instead of secondo me?

You can, and it is grammatically correct, but secondo me (literally 'according to me') is much more common and natural in everyday Italian for expressing 'in my opinion'.

How would I change this sentence to say 'His idea makes NO sense'?

You would say La sua idea non ha nessun senso. Notice that we use the chopped-off form nessun because senso is a masculine noun starting with a single consonant. Also remember that Italian uses a double negative here: non goes before the verb, and nessun goes before the noun.