Diary - One of my friends shared an interesting conversation

[Maybo]

This is an entry from my diary. Please check it and correct any mistakes.

One of my friends shared an interesting conversation with me today. She said this afternoon she had lunch with her two colleagues, Mary and Lucy. Mary said, "I don't want to eat the baby shrimps because they are very young and it's cruel to eat them. Then, Lucy asked, "why did you eat baby pigs?" Mary explained, "Baby pigs are bigger than baby shrimps." Lucy retorted, "but baby pigs are young too, although their size is bigger than that of shrimps. Why would you eat them?" Mary didn't answer. My friend wanted to laugh but she held it.

 

[emsr2d2]

One of my friends shared an interesting conversation with me today. She said that this afternoon she had had lunch with her two of her colleagues, Mary and Lucy.

I'd change "today" to "just now" or "this evening". "Today" could mean any time today. We have to wait until the next sentence before it becomes clear that you're talking about a conversation that took place sometime after "this afternoon".

Mary said, "I don't want to eat the baby shrimps because they are very young and it's cruel to eat them".

You omitted the closing quotation marks. It's tautologous to point out that "baby anything" is very young. That's literally what "baby" means.

Then, Lucy [then] asked, "Why did do you eat baby pigs?"

You didn't need "then" at all. If you really want to use it, put it where I've indicated above.
Saying "Why did you ...?" would be fine if Mary had just finished eating a meal made of baby pigs. I don't think that's what your friend meant. She wanted to know why Mary, habitually, is prepared to eat piglets. For that, we use the present tense.

Mary explained, "Baby pigs are bigger than baby shrimps." Lucy retorted, "But baby pigs are young too, although their size is they are bigger than that of shrimps. Why would you eat them?" Mary didn't answer. My friend wanted to laugh but she held it in.

If this is your record of a real conversation in English and your friend actually said "... although their size is bigger than that of shrimps", then that's OK (reported speech). However, you might want to tell your friend that what she said is unnatural. There's no reason to say "The size of XXX is bigger/smaller than that of YYY". We just say "XXX is bigger/smaller than YYY". We know that "big(ger)" and "small(er)" refer to size.

Did this conversation take place in English or is this your translation?

Note that baby pigs are called piglets. I don't think there's a specific name for baby shrimps.

 

[Maybo]

Did this conversation take place in English or is this your translation?

It is my translation.

 

[emsr2d2]

It is my translation.

OK, then consider my changes corrections to your translation.