Maybe it's a normal sign of the fall ............ Some of my trees leaves are turning yellow and falling off to. In New York

Probably a few chilly nights = yellowing leaves. Very short season....Memorial Day to Labor Day, basically, and, we're done.

Frank
Bronx, NYC
Zone-7b

ColMon ,
It looks fairly normal for this time of year up here in NH.
A few of my leaves look similar, but most are still normal green.
Nothing to worry about really.

OK.. Is it ok to leave it outside still, or should I bring it in asap?

ColMon ,
If you want to let it go dormant and store it for the Winter in a place with temps no lower than 25F and no higher than 45F , then leave it out until it gets a couple of light frosts.
Then move it in a garage etc. to protect from more or harder frosts and allow it to finish dropping its' leaves.
Then move it to the spot it will stay for the Winter.
Where you are in NH , you should be able to leave it out at least another month or longer.
Think of what you are doing as ripening the wood for Winter.

Also... what are the defining differences in the "Italian Fig" strain? I'm very new to gardening in general.. I happen to really fall in love with this tree.
How big should I expect it to get?

Italian fig could be many things depending on where you bought it.
Fig variety ID is sometimes possible if you post pictures of most common leaf shape and a ripe fruit whole and cut in half displayed with a quarter coin to give a sense of scale.
Post both here and at figs4fun forum to get the highest chance of someone knowledgeable being able to ID.
You can prune and shape the tree anyway you like and keep it as small as you want to be able to easily reach the fruit and to store it for Winter if you keep it in a pot.

50 days ago a few of my leaves look similar, but most are still normal green.
today may fig tree is very strong
don't worry ����