tThe time is set at 6pm every day.

Remember, always capitalize the first letter of every sentence.

tTo be honest, I can't stand him sometimes since we have polar opposite opinions about politics and other stuffs.,

but I know deep down that these times are precious.

Never start a sentence with “but” or “and.”

he'He’s not gonna live too long.

andSo I have to cherish these moments before his time comes.

My (usual) dinner time is around 6pm.

Sounds more natural to add the word "usual" here. Otherwise it kind of sounds like you're only talking about today.

I usually eat dinner with my father and occasionally with my bigolder brother who lives in a separate township.

"big brother" is sort of a childish way of phrasing it. "older brother" can be used by anyone.

tThe time is set at 6pm every day.

"set at" isn't needed here.

It's a habit of my father to set theinsist on a set time for eating food, taking meds or watching TV.

More natural phrasing

Dinner time (also) means conversation time with him.

Added a word to sound more natural

We love each other, but we are not too close or open about our feelings.

But, during dinner time and lunchtime, he'd shares his stories about his upbringing in rural areas, about how hard he and mum had to work to put food on the table.

"dinner time" / "lunch time"
"dinner" / "lunch"

Sounds more natural if you're consistent on including time or not including time.

"He'd share" sounds like something he habitually did in the past. Talking about your father in the past tense makes like this it sound like he's dead or otherwise no longer around.

He's very short tempered and doesn't like it when I try to interrupt whilen he's talking.

tTo be honest, I can't stand him sometimes since we have polar opposite opinions about politics and other stuffs.

"stuff" is already plural in standard English.

"stuffs" is sort of slangy/childish

bBut I know deep down that these times are precious.

hHe's not gonna live too long.,

and I have to cherish these moments beforeuntil his time comes.

I think until just sounds a little better than before as it emphasises the continuous nature a bit more.

Dinner tTime with mMy fFather

Important words in a title have a capital letter.

tThe time is setfixed at 6pm every day.

Sentence must start with a capital letter. Think 'fixed' sounds better than 'set'.

Dinner time means conversation time withfor him.

We love each other, but we are not toovery close or open about our feelings.

But, during dinner and lunchtime, he'd share his stories about his upbringing in rural areas, and about how hard he and mum had to work to put food on the table.

Use 'and' to connect these two parts together.

tTo be honest, I can't stand him sometimes since we havare polar opposite opinions abouts when it comes to politics and other stuffs.,

'stuff' is uncountable so should be singular. Use , to link to next sentence.

hHe's not gonna live too long.,

Sentence starts with capital letter. As next sentence starts with 'and' use a , to join.

My dinner time is around 6pm every day.

If you add the "every day" here, it would avoid the redundancy of the later sentence.

I usually eat dinner with my father and/dad, but occasionally I'll eat with my big/older brother who lives in a separate township.

"dad" would be appropriate if you want to sound casual. If your big brother joins you and your dad, it'd be better to say "but occasionally, my big brother will join us too." It sounds like you usually eat dinner with only your dad, but sometimes you eat with only your brother.
"and" isn't incorrect. However, "but" creates a natural sounding contrast between the usual (you and your dad eating) and the occasional (eating with your brother/your brother joining).
"big brother" has a less mature sound to it than "older brother", both are fine.

the time is set at 6pm every day.

This sentence is a bit redundant because your first sentence established that your dinner time is at 6 every day.

It's a habit of my father to set the time for eating food, taking meds or watching TV.

He's practically a robot in disguise because everything has to go according to his schedule or he will freak out.

Ha! This is very natural sounding

But, during dinner and lunchtime, he'd share his stories about his upbringing in rural areas, and about how hard he and mum had to work to put food on the table.

tTo be honest, I can't stand him sometimes since we have polar opposite opinions about politics and other stuffimportant topics.

A bit of a personal flourish from me, but I think this would express what you're trying to express.

butHowever, I know deep down that these times are precious.

You could also say "this time we spend at dinner is" and sound pretty natural

hHe's not gonna/going to live too much longer.

This gives the sense that he's terminally ill, or he has a foreseeable timeframe during which he'll pass away.
Something like "He won't live forever" communicates that he's older but does not have a foreseeable timeframe during which he'll pass away.

and I have to cherish these moments before his time comes.

tThe time is set at 6pm every day.

tTo be honest, I can't stand him sometimes since we have polar opposite opinions about politics and other stuffs.

bBut, I know deep down that these times are precious.

hHe's not gonna live too long.

and I have to cherish these moments before his time comes.

My dinner time is around 6 pm.

tThe time is set at 6 pm every day.

But, during dinner and lunchtime, he'd shares his stories about his upbringing in rural areas, about how hard he and mum had to work to put food on the table.

Since this seems to be an ongoing habit rather than a past one, I have changed your verb to present tense.

tTo be honest, I can't stand him sometimes since we have polar opposite opinions about politics and other stuffs.

bBut I know deep down that these times are precious.

hHe's not gonnaing to live too long.

You can say "gonna" orally, but in written English we use "going to" until it's a direct quote.

andSo I have to cherish these moments before his time comes.