Today is my father’s birthday, but we didn't buy a birthday cake to celebrate for him this year.

When it comes to the birthdays, I find that as we get older and older, we care about it less and less.

When I was a child, every time when it was thesomeone's birthday of one of ourin the family, my father always asked us to buy a cake and we did so enthusiastically.

And we did it with a thrilled mood.

My younger sisters and I havare studiedying in the same city, so we plan to return together.

We expected to take the train at about 3 p.m., however, we took the train at 7 p.m. We ovinstead. We underestimated our own ability to procrastinate.

or

We expected to take the train at about 3pm, however, we took the train at 7pm instead. We underestimated our ability to procrastinate.

Even though I packed up some of the luggages in advance, I still had to spentd more time on it than I had expected.

If my sisters didn’t have important things to do at the university, we would gohave gone back tomorrow.

This is subjunctive tense.

Today is my father’s birthday, but we didn't buy a birthday cake (to celebrate) for him this year.

When it comes to the birthdays, I find that as we get older and older, we care about it less and less.

"Birthdays" instead of "the birthday" because you're talking about birthdays in general.

When I was a child, every time when it was the birthday of one of our family members, my father always asked us to buy a cake.

Or "..every time when it was the birthday of someone in our family..."

My younger sisters and I havare studiedying in the same city, so we plan to return together.

"Have studied" makes it sound like you guys are no longer studying in the same city, but you used to. In that case, you guys wouldn't have been able to return together.

We expected to take the train at about 3 p.m, however, we took the train at 7p.m. We ovunderestimated our own ability to procrastinate.

Even though I packed up somthe luggages in advance, I still spent more time than I expected.

Luggage is both singular and plural. You could probably use "luggages" somewhere, but I don't know where and I've never seen "luggages" used before.

If my sisters didn’t have important things to do at the university, we would go back tomorrow.

When it comes to the birthdays, I find that as we get older and older, we care about ithem less and less.

And we did it with awere thrilled moodto do it.

Even though I packed up some luggageof my things in advance, I still spent more time than I expected.

We just did it at a very slow speedly and even ate some snacks.

Today is my father’s birthday, but we didn't buy a birthday cake to celebrate for him this year.

When it comes to the birthdays, I find that as we get older and older, we care about ithem less and less.

When I was a child, every time when it was the birthday of someone ofin our family, my father always asked us to buy a cake.

Either "someone in our family" or "one of our family members" would work here.

And we did it with awere thrilled moodto do it.

My younger sisters and I havare studiedying in the same city, so we plan to return together.

I was unsure at first, but reading further it sounds like you are all currently studying in the same city, rather than having studied in the same city in the past.

We expected to take the train at about 3 p.m, however, we took the train at 7p.m. We ovunderestimated our own ability to procrastinate.

It's definitely tricky, but if you procrastinated for more than you thought you would (which is what taking the later train implies) then you underestimated rather than overestimated your ability to procrastinate.

Even though I packed up some luggages in advance, I still spent more time packing than I expected.