I don't know exactly when or howknow how or when he joined the government workforce.

Your sentence wasn't necessarily incorrect, just that word ordering of "I don't exactly know how or when" is slightly more common. "I don't exactly know when or how" is also common.

Since he passed away decades ago, it has remained a bit of a mystery to me.

This suggestion is not necessary to make the sentence correct, it's just slightly more accurate. Since otherwise, it sounds like "it remains a mystery" for "everyone" rather than just you/you and a few others. Of course, if you did intend to mean that this is a "mystery for everyone," then your sentence would be accurate as is.

If he wasn't too busy at work, he would spend more time at home and help my mother with the farm work.

Not necessarily incorrect, just that "help with the farm" is more common than "help with the farm work," and they both mean the same thing.

He commuted to and from work by bike.

Combining the above sentence with this one into "He had a bicycle that he used to commute to and from work with." Sounds a little less redundant.

He also was fond of Chinese calligraphy.

This sentence sounds a little bit jarring (off/weird) without the "also," because it's seemingly unrelated to the previous sentences. So adding "also," helps to indicate that you're changing topics.

In his spare time, he liked to practice it.

If you remove the period from the above sentence and continue this one with "and in his spare time, he liked to practice it." It would flow a little bit better.

Just like other male villagers, he also played mahjong, drank Chinese liquor, and smoked, but not excessively.

Correct as is, I just personally prefer to put asides in parenthesis "and smoked (but not excessively)." It's just a personal preference, and not necessarily even proper English grammar (I think the "correct way" is to use one of ;, :, or -, but I never learned how to properly use those, nor have most Americans).

Amongst my three siblings and meI, he favored me the most because I studied hard and did well academically.

The first impression my father left on me was that he was tall, thin, and looked frail.

Thought your sentences was grammatically correct, we usual use impression for new things. Ex. A) What did you think of the applicant? B) My first (initial) impression was…
Try: One of the oldest things I remember about my father was that he was tall, thin, and looked frail.

He was an employee of the local government employee.

My grandparents and their ancestors had all been farmers.

My family has come from a long line of farmers. We have always been farmers.

I don't know exactly when or how he joined(or why) he started working for the government workforce.

Since he passed away decades ago, it has remained a bit of a mystery.

He passed away decades ago so it has been a bit of a mystery.

If he wasn't too busy at work, he would spend more time at home and help my mother with the farm work.

When he wasn’t too busy at work, he would spend more time at home helping my mother with the farm work.

Often, when he came back home, there would be a bag of candies hanging on the left handlebar of his bike.

When he came home, he would often leave a bag of candies hanging on his bike’s left handlebar.

It was said that he often had stomach problems.

I’ve been told / I’ve heard he often had stomach problems.

Just like other male villagers, he also played mahjong, drank Chinese liquor, and smoked, but not excessively.

Just like other men in the village, he also played mahjong, drank Chinese liquor, and occasionally smoked.

Among my three siblings and me, he favored me the most because I studied hard and did well academically.

He favored me the most out of his four children because I studied the hardest and did well academically.