Winter vacation beginshas begun! Winter vacation has begun!

WI began my winter vacation begins! I began my winter vacation!

Winter vacation begins! (today)! / Winter vacation has begun! Winter vacation begins (today)! / Winter vacation has begun!

If it already started; use 'has begun' because it came before all the other past events you are describing in this journal

I saw many "pineapple babies" when I returned to my apartment by foot. I saw many "pineapple babies" when I returned to my apartment by foot.

more natural: when I walked back to my apartment

I saw many "pineapple babies" when I returnedas I walked back to my apartment by foot. I saw many "pineapple babies" as I walked back to my apartment.

I saw many "pineapple babies" when I returned to my apartment byon foot. I saw many "pineapple babies" when I returned to my apartment on foot.

"On foot" is the set phrase in the US but this is a better sentence: I saw many "pineapple babies" when I walked back to my apartment.

The university I study at is surrounded by many pineapple fiarms. The university I study at is surrounded by many pineapple farms.

The university where I study is surrounded by (many) pineapple fiarms. The university where I study is surrounded by (many) pineapple farms.

“Many” isn’t wrong but is also unnecessary since “surrounded by farms” already implies that there are many of them.

The university I study at is surrounded by many pineapple fiarms. The university I study at is surrounded by many pineapple farms.

The university I study at is surround by many pineapple firms/ farms(?). The university I study at is surround by many pineapple firms/ farms(?).

Maybe you meant 'farm' instead of 'firm'

The university where I study is surrounded by many pineapple firms. The university where I study is surrounded by many pineapple firms.

As a result, I can see them growing process of themin real-time. As a result, I can see them growing in real-time.

As a result, I can see their growing process of them| I can watch them grow. As a result, I can see their growing process | I can watch them grow.

As a result, I can see their growing process of them. As a result, I can see their growing process.

As a result, I can see their growing process of them. As a result, I can see their growing process.

As a result, I can see their growing process of them. As a result, I can see their growing process.

I like pineapple, but if I eat too much it hurts my tongue, so I prefer its processed product: pineapple cake! I like pineapple, but if I eat too much it hurts my tongue, so I prefer its processed product: pineapple cake!

To most Americans, “pineapple cake” is something like pineapple upside down cake, which is a cake with pieces of pineapple baked into its top crust: https://www.backtomysouthernroots.com/homemade-pineapple-upside-down-cake/ If you mean 鳳梨酥, I would call those “pineapple cookies” in the US.

It tastes perfect and I like it so mucha lot. It tastes perfect and I like it a lot.

I relaxed and made a study(ing) plan. I relaxed and made a study(ing) plan.

“Study plan” is more natural.

During my break, I relaxed and made a studying plan. During my break, I relaxed and made a study plan.

I relaxed and made a studying plan. I relaxed and made a study plan.

We use "study plan" in the US.

I also scheduled my winter vacation, too plans. I also scheduled my winter vacation plans.

I scheduled winter vacation, too. I scheduled winter vacation, too.

This sounds like you made plans to take a winter vacation sometime in the future, which doesn’t really make sense, since you said winter vacation had already started. Maybe you mean, “I made a daily (or weekly) schedule that I plan to follow throughout this winter vacation,” or maybe “I planned some winter vacation activities,” or…?

I scheduled winter vacation, tootook time off from my job as well during the holidays. I took time off from my job as well during the holidays.

I think this is what you mean, but please let me know if it's wrong.

I hope I can be productive on / during this vacation. I hope I can be productive on / during this vacation.

I hope I can be productive on this vacationduring the holidays. I hope I can be productive during the holidays.

I hope I can be productive onduring thisat vacation, too. I hope I can be productive during that vacation, too.

I can't tell whether you're on vacation now or whether you want to be productive during your just scheduled winter vacation.