He is moving to another prefecture in April for his job, so our parents are planning thea family dinner before he leaves.

He and I had decided to give some presents at theat time to show our appreciation, (and that's/which) is why we hung out today.

I think "and that's" is more natural, but "which" is ok too. If you use "which" you don't use "and" in this cause and effect pattern.

There is a sort of older/formal construction "and which ..." which is used for providing extra information about a thing you've just introduced

It was not easy to choose their gifts because we knew that our parents have often told us that they didon't need any new stuff.

"didn't need any new stuff" leaves open the possibility they've changed their minds, or that they've died, which I don't think is what you're going for. If you still believe that to be their viewpoint, it's better to talk about the viewpoint in the present tense.

Eventually, we got slightly expensive but beautiful chocolates, a pair of small dishes, and two blank booklets.

Why is itare there 39?

Because in Japanese, we pronounce 3 as "san" and 9 as "kyuu/Q," whichso the pronunciation is similar to "thank you."

Now our next tasks are coming up, and we are writing many messages to them.

He is moving to another prefecture in April for his job, so our parents are planning thea family dinner before he leaves.

He and I had decided to give them some presents at the time to show our appreciation, and which is why we hung out today.

It was not easy to choose their gifts because we kneow that our parents often toldell us that they didon't need any new stuff.

Changed a few things to present tense, because it is a recurring activity. If it remains past tense, it might indicate that your parents have passed away.

Because in Japanese, we pronounce 3 as "san" and 9 as "kyuu/Q," which makes the pronunciation is similar to "thank you."

Now our next tasksignments are coming up, and we are writing many messages to them.

I'm not entirely sure what you mean by "tasks" here, mostly because I may be missing context about the job system in Japan. I did my best to provide a reasonable synonym that sounds natural.

He is moving to another prefecture in April for his job, so our parents are planning thea family dinner before he leaves.

He and I had decided to give them some presents at the time to show our appreciation, and which is why we hung out today.

It was not easy to choose their gifts because we knew that our parents often told us that they didn't need any new stuff.

Now our next tasks are coming up, and writing many messages to them.

I'm going to offer a few possible edits.

Now our next task is to write many messages to them.
Now our next tasks are coming up, such as writing many messages to them.
One of our next tasks is to write many messages to them.

These would each have better grammar, but the meaning varies slightly with each. Pick whichever one you think best!