I planned to check my understanding of this book, so I took the quizzes at the end of the pages.

You've already mentioned the book, so we can infer that the understanding you refer to here is of the book

It i's a basic grammar book, so I thought I should have gotten a better result.

Contrary to the other comment I think there's a meaningful difference between "would" and "should"
"I thought I would have gotten a better result" implies that you assumed that your result will be good and are surprised you didn't.
"I thought I should have gotten a better result" implies that you are disappointed in yourself and wanted to do better.
These are similar but one (should) feels more humble to me.

I discussed these with AI and got help.

Nothing wrong with the writing here, just want to say to be *very* careful using AI. It is often wrong in misleading ways and unless you know what it's talking about in great detail it's hard to identify when it is wrong. I would not trust it as a source of information that you want to learn.

I had another big plan today, which isOne of those plans was celebrating Bento Box Day.

You mentioned having other plans in the previous sentence so linking this sentence to the previous one flows a little more naturally.

A colleague and I have on this daycelebrated it since April this year.

This sentence is a little difficult to interpret. Since you specify when you celebrate it in the next sentence you can remove that part to simplify this sentence a bit.

EveryAt the end of theeach month, we gather at each other's homes and make bento for the next day's lunch together.

This way flows more naturally.

It is sSometimes it's Asian food, and sometimes European food, due to our backgrounds.

Personal feeling that having "sometimes" at the start is more natural. Also using contractions like "it's" feels more natural in most cases.

We've been on vacation nowrecently, so we didn't need to make "lunch".

Struggling to interpret what this means since you mention making lunch in the next sentence.

SoBecause of this, we were going to make Focaccia at her home, and I brought Soba noodles for our lunch.

Avoiding repetition of "so"

I hadve no idea at all about baking, so I just felt sorry about it.

If you still don't really know much about baking, then it is better to express that in present tense. Using past tense implies that at the time you didn't but that now you do (or at least might).

We made small waffle cups with the cookie and put the ice creams we bought earlier in them.

When using "put" you generally need to specify what you put the object in.

The dough rising was longertook longer to rise than we expected, so we played a board game while we were waiting.

Rephrased to be more natural.

In fact, during the baking time, I asked them so many things about English - folding dough, lukewarm water, etc. - but they never showed me any disappointment, or acted like a parents.

These were really small things, but also really, but they were enormous things foro me.

The original sentence makes sense, but this is how I would phrase it.

I can't saynot express how wonderful they are.

Instead of "say", "express" feels more appropriate here. I'd also say this is one of a few cases where not using the contraction is more natural. Not using the contraction here provides additional emphasis.

I started my day early today.

The "today" feels redundant to me because you put "my day." Another alternative sentence could be "I started today early" to let the reader know that you're talking about the current day.

I planned to check my understanding of ithis book, so I took the quizzes at the end of the pages.

Because you already mentioned the grammar book in the last sentence, you can replace "the book" with it so it's more concise and natural sounding.

It i's a basic grammar book, so I thought I shwould have gotten a better result.

The contraction "It's" sounds more natural and so does "would." I wish I had a better explanation. Sorry.

I had another big plan today, which is Bento Box Day.

A colleague and I have celebrated it on this day since April.

I also think you should clarify what you mean by April. Do you mean April of this year? Last year? When? I'm not sure I understand completely what you're trying to say here.

Every end of the month, we gather at each other's homes and make a bento for the next day's lunch together.

It i's sometimes Asian food, and sometimes European food, due to the difference in our backgrounds.

Similar to the other sentence, "it's" just sounds more natural here. Also I put "the difference" to clarify more, but that part sounds good and makes sense without it.

We've been on vacation now, so we didn't need to make "lunch".

It's not clear why you're using quotation marks here around the word "lunch." It's it something sarcastic or a direct quote of someone? If not, there's probably no need.

Also, we stopped by an Asian grocery market and bought 5 different flavours of ice cream!

Just a note on the word flavors. I assume you're going for the British spelling, but if you're going for the American spelling, it should be "flavors."

I had no idea at all about baking, so I just felt sorrybad about it.

The words "sorry" has the feeling as if you did something wrong, but "bad" has the feeling of pity which seems more appropriate here.

It wais an Italian cookie, and I heard about it for the first time.

Because you're explaining what a Pizzelle is, you'll want to talk in the present with "is" instead of "was."

It lookeds like a waffle, and it was good!

Similar explanation to the last sentence.

We made small waffle cups with the cookies and put the ice creams we bought earlier.

The word "ice cream" is both singular and plural.

Aa bag of olives and a book:, Le Petit Prince.

I would merge this and the last sentence, adding a comma after "them" and before "a." Also use of a colon is more for a series of items. A comma is more appropriate here.

As for the book, shmy colleague, some other colleagues, and I have a weekly French chat about it in the morning.

This is what I think you were trying say. I used "my colleague" instead of "she" to remind the reader of who you were talking about because that colleague hadn't been mentioned in the last couple of sentences. It's like a little reminder of who you're talking about.

Also, because you have "As for the book" in the beginning, the rest of the sentence feels off because you haven't connected it to the rest of what you're talking about. So I added "it."

We shared stories about our recentpast few days.

Sounds more natural.

They were always warm and kind to me, and I really appreciated theat moment with them.

Sounds more natural.

In fact, during the baking time, I asked them so many things about English - --folding dough, lukewarm water, etc. - --but they never showed me any disappointment,. They acted like parents.

It's a small detail but the double dash, not the single one, is used in this case, with no spaces.

They showed me what the "folding" is, and guided my hand to let me feel what "lukewarm" is.

These were really small things, but also enormous things for me.

I can't say enough how wonderful they are.