I thought of goingintended to thgive theater atickets as gifts for Mother's Day and Father's Day.

From your original text, I think you meant giving theater tickets as gifts.

I asked them which performances they want to watch while looking at a list of the showsWhile looking at the theater's performance schedule, I asked my parents, and they said they would like to listen to Tsurube's rakugo.

Combine the sentence.

Then they said that they would like to watch Mr. Tsurube’s rakugo show.

Combine the sentence.

When I tried to buy tickets online on the release day, they were sold out within 10 minutes after they went on sale.

When IAt the time of release, whent to the sales page at the time of release, I got I tried to navigate the sales page, I received a message asksaying me to try again becausthat the access was concentrated and to try again.

At the time of release, when I tried to navigate the sales page, I received a message saying that the website was experiencing high traffic and to try again.

While I was flustered, I couldn't buy it because it was sold outIn the midst of my flustered state, the sales ended, and I couldn't make the purchase.

It’sWhat a shame.…

I will stryive to be able to buy if I had a next chancethem if there is another opportunity.

( Today / Recently ), I thought of going to the theater with my Mum and Dad as a gift for Mother's Day and Father's Day.

Or:
"Today, I took my Mum and Dad to the theater to celebrate Mother's and Father's Day."

I asked them which performances they wanted to watch while looking at a list of the shows.

Then they said that they would like to watch Mr. Tsurube’s rakugo show.

Rakugo is traditional ( form / type ) of Japanese comic storytelling.

( But ) When I tried to buy tickets online, they were sold out within 10 minutes after ( they went / going ) on sale.

When I went to the sales page at the time of release, I got a message asking me to try again because access was concentrarestricted.

While I was flustered, I couldn't buy it because it was sold out.

I'm not 100% sure what you mean with "flustered" here.

I will try to be able to buy if I had a nextuy it the next time I get the chance to.

I thought of goingtaking my parents to the theater as a gift for Mother's Day and Father's Day.

The subject needed a bit of clarification and the sentence is a bit odd because these are two different days.

I asked them which performances they would want to watch while looking at a list of the shows.

Then they said that they would like to watch Mr. Tsurube’s rakugo show.

When I tried to buy tickets online, they were sold out within 10 minutes after they wentof going on sale.

When I went to the sales page at the time of release, I got a message asking me to try again because access was concentrarestricted.

The word "concentrated" doesn't make sense here, and I'm not sure what you intended for the meaning of this sentence. I took a guess at what a replacement word could be, but I could be off from what you meant to say.

While I was flustered, I couldn't buy it because it wasBy the time I got to the sales page, I couldn't buy any tickets because they were sold out.

Using "flustered" doesn't feel quite right here. I think you need to clarify what you were doing as the tickets were sold out.

It’s a shame., (but I'll try to buy tickets again if I get another chance.)

This should be combined with the sentence below. Otherwise, it feels a little too bare on its own.

I wi'll try to be able to buy if I had a nextuy tickets again if I get another chance.

This should be combined with the sentence above

I thought of goingabout taking my parents to the theater as a gift for Mother's Day and Father's Day.

Theater = US
Theatre = rest of world

I asked them which performances they wanted to watch while looking at a list of the showings.

Shows is also ok, but showings is better for the theatre.

When I went to the sales pagebuy them at the time of release, I got a message asking me to try again because access was concentrarestricted.

While I was flusteredssing, I couldn't buy it because it was sold out.

I will try to be able to buy if I had a nextsee if I can buy them again if I get another chance.