I looked atup the phone number online, but I didn't get any information about it.

"Look up" would mean finding information about something, while "look at" means to examine something in front of you.

I didn't call back because there weare many disturbannoying phone calls nowadays, for things such as selling insurance, selling houses and pushing loans.

"Nowadays" is in the present, so the present tense is needed.
"Disturbing" may not be the best word: it would mean that there is something about the phone call that you find scary or unsettling, not that it just disturbs what you are doing.
I think it would also be better to write something like "annoying phone calls from unknown numbers." That's clearer.

I was wondering if someone had had an emergency.

It turned out that it was my second sister-in-law who called me.

This is grammatical, but "second sister-in-law" isn't really a phrase that we would use in English, not unless we were talking about a number of different sisters-in-law.

She asked me to go to my mom's house to have lunch together with them.

The original is grammatical, but this is better.

I dihadn't planned to have lunch at my mom's house this afternoon at first, but I haved to go to at current situation.

The past perfect is more appropriate for "planned" because it was no longer the case that you had no plans to have lunch at your mother's, and that action (having no plans to do something) took place further in the past, not necessarily right before the other events here.

You can also just remove "this afternoon." "This noon" isn't idiomatic: we would say either "this afternoon" or "at noon."

From the rest of the journal, it sounds like you already went, so "have to go" must also be in the past tense.

I was born and raised in a small village where my second sister-in-law and her son live now, andbut I rarely go back to the village[there].

"But" sounds more appropriate as that part of the sentence has a slight contradiction with the first part.

The topics awere mainly about things related to our villagers.

The rest of the narration is in the past tense, so the past tense should be used here too.