PI played badminton with new friends!

I had a badminton game date with my friends, Qian and Ling, b. Both in theof my friends major ofin anaesthesia.

We already know badminton is a game. Your friends college major is a separate subject and deserves to be a separte sentence. There is also some grammar problems.

I arrived at the gym on the scheduled time.

This is a normal structure for this statement. I arrived at (the) _______ on time.

They saw me and then asked:"Are you Joey?

Nice to meet you here."

All of them were incredibly convivalfriendly and quick-witted.

Convival is a word that is rarely seen or used, most native english speakers do not know this word.

I felt a little awkward asbecause I didn't know their names.

I gave a look of help to Qian secretlydiscretely gave Qian a look of help, wishing she could tell me the names of these lovely guys.

Discrete would be more appropriate because you do not want others to see. Also I'd use handsome and funny rather than lovely. It's just a preference.

Qian whispered to me like:"Look at that guy wearing a pair of glass?".

AndIn that way, she introduced me to everyone here to me in that kind of way.

I kept themir names in mind and was able to match them with their namfaces.

It's common for native english speakers in America to say, "To match a name to a face". So this combination, a name... to a face, is common and understood.

We sweated passionately on the pitch and cheered fo, becoming excited over every good shotplay.

Cheering is something that spectators usually do. If you were playing it would be more appropriate to say you were excited. Badmintons have 'hits' rather than shots. In this context I would use the term play. In the context it is a noun a describes a series of hits.

When the gym-keepThe gym's manager was walking round to. She announced she was going to close the gym, so we knew it' was time to leave the gym and went to get something to eat.¶
¶
When the gym manager announced she was going to close the gym, we jbew us was time to leave and geat something to eat.

I wrote two examples. What you wrote doesn't sound natural, but it is mostly correct. "We knew it's..." It was can not form a contraction.

CAfter excersing for such a long time, chicken hot pot seemed so appealing as w. We were so hungry after exercise such a long time.

It seems like you are practicing a certain type of grammatical structure. I'd say, do not be afraid to break up these statements into smaller sentences.

All in all, we had a whale of agrand'ole time last night.¶
¶
All in all, we had a grand old time last night!.

I've never heard this phrase before. A grand'ole time is a phrase commonly used. It means that the night was fun and memories were created as well as reminding someone of past good times.

Playing badminton with new friends!

I had a badminton game date with my friends, Qian and Ling, both in the major of anaesthesia.

What you wrote works. But if you wanted it a little more natural you could say, "both majoring in anaesthesia."

I arrived at the gym onat the scheduled time.

I gave a look of help to Qian secretlyQuian a pleading look, wishing she cwould tell me the names of these lovely guys.

Qian whispered to me like:"Look at that guy wearing a pair of glasses?"

And she introduced everyone there to me in that kind of way.

When the gym-keeper was walking round to annouce she was going to close the gym, we knew it' was time to leave the gym and eat something.

Chicken hot pot seemed so appealing as we were so hungry after exerciseing for such a long time.