As a tropical country, Indonesia is famous for theits variety of fruits.

Right now in January,(, it) is the best time to buy and enjoy durians since it's their peak harvest season.

If you use a comma here, you need the "it" to make the part after the comma appear complete. If you don't use the comma, you don't use the it.

When buying a fruits in their peak harvest season, we manage to get them inat a more affordable price because the supply is greater than the demand.

Countable fruits is less common than uncountable fruit (and is usually used when discussing plants in a more scientific context).

Some central durian production areas would hold a day with a free or even all-you-can-eat experience to gainattract customers from another city.

"gain" is valid here, but "attract" is more natural in this context.

Enjoying durians with family is also (one part of a local culture / a local tradition / one of the local traditions) that nurtures a quality time within a big family.

There's a couple of options here, that all have a slightly different feel:

"one of the local traditions" implies that there are other (specific) traditions that focus on family time
"one part of a local culture" focuses a bit less on this specific tradition and more on the wider culture of the area.
"a local tradition" is the most neutral option, with no other meanings

As a tropical country, Indonesia is famous for thehaving a variety of fruits.

I think "its" as suggested by the other user is okay too, but it gives me more the feeling of Indonesian fruits being something I've already been introduced to.

Since there's no winter, we can grow them throughout the whole year.

"whole" is a little redundant here because "throughout the year" is already a set phrase, but this sentence is good!

Many of them are seasonal fruits, where so we can enjoy them within specific periods.

Right now, in January, is the best time to buy and enjoy durians since it'this is their peak harvest season.

I think the "in" can be omitted.

it's -> this: "it" is rather neutral, but for "now" things, I'd strongly prefer "this".

When buying a fruits in their peak harvest season, we managare able to get them in a more affordable price because the supply is greater than the demand.

"manage to" makes it sound to me like it's somehow a struggle, you still have to shop around but somehow you'll manage to find a good price. But it sounds like you're just saying they are offered at a cheaper price due to supply and demand. "able to" is more neutral to me, conveying that it is possible, or that you have opportunity in this time period.

Some central durian production areas wouldill even hold a day with a free or even all-you-can-eat experience to gainet customers from another city.

"will even" gives me a more "special" feeling, that this isn't something that happens everywhere or every day. "Some places hold a durian festival, but some go even further and let you eat all you can!"

Please disregard if that's not the intent you were going for, though.

Enjoying durians with family is also one of a local culture that nurtures a quality time within a big family.

Time is not quantifiable so we don't use any articles like "a" or "the".

As a tropical country, Indonesia is famous for theits variety of fruits.

Since there's no winter, we can grow them throughout the whole year.

Many of them are seasonal fruits, whereich we can enjoy them with during specific periods.

Right now, in January, is the best time to buy and enjoy durians since it's their peak harvest season.

When buying a fruits during their peak harvest season, we manage to get them inat a more affordable price because the supply is greater than the demand.

Good use of supply vs demand expression

Some central durian production areas would hold a day with a free or even all-you-can-eat experience to gain customers from another cityies.

Enjoying durians with family is also onepart of aour local culture that nurtures a quality time within a big family.