Sso we often played table tennis with our textbooks. so we often played table tennis with our textbooks.

I suggest combining these two as "We often played table tennis with our textbooks because we couldn't afford rackets."

On the other hand, one of the students had a relatively wealthy family. On the other hand, one of the students had a relatively wealthy family.

Adding a transition phrase or word will prevent awkward sentences. i.e: 'to contrast', 'similarly'

His father worked in the local supply and marketing cooperative, which meant his father had a salary. His father worked in the local supply and marketing cooperative, which meant his father had a salary.

Saying 'had a salary' could mean the father just has an income, not that it's a wealthy or great amount. I suggest adding a word to describe it if you want to emphasize or point out that the father makes a lot of money.

His father worked in the local supply and marketing cooperative, which meant that his father had a good/high/decent salary. His father worked in the local supply and marketing cooperative, which meant that his father had a good/high/decent salary.

* maybe put "good salary" or "high salary" or "decent salary" if you meant he was rich. -> connect sentence

S... so the student had a pair of rackets. ... so he had a pair of rackets.

* since "so the student had a pair of racket" is not a complete sentence. (only stating reason) Or you could do: "So, the student had a pair of rackets."

After I started studying in middle school, I found there was a “table tennis table” outside my classroom. After I started studying in middle school, I found there was a “table tennis table” outside my classroom.

Instead of writing "table tennis table" (since it can be difficult to say out loud,) I would phrase it "I found there was a "table" for table tennis outside my classroom." or you could describe the makeshift table in the same sentence.

Although it was not a real table tennisn manufactured table, table tennis could be played on it. Although it was not an manufactured table, table tennis could be played on it.

I'd say this is good. Avoid repeating words too often as it can be difficult to pronounce, mentioned above. It makes sense so this is fine to keep this way.

Because there was only one table tennis table for my class, it was common to see a few students competing for the chance to play itable tennis. Because there was only one table tennis table for my class, it was common to see a few students competing for the chance to play it.

Good structure, just the same about repetition. You have context as to what the students are competing for, so it wouldn't be entirely necessary to include it again.

The grades I achieved in the middle school graduation exam would determine whether or not I could work for the government. The grades I achieved in the middle school graduation exam would determine whether or not I could work for the government.

So, I dared not play table tennis often. So, I dared not play table tennis often.