A sea trip / A trip to the sea

My family areis going to have a summer vacation that is kind of far from my home. / My family is going on summer vacation somewhere a bit far from my/our home

In American English, "family" is always singular so we use "family is". In British English, "family" can be either plural or singular

We’re going to have a 1 week sea trip about. / We're going to have a sea trip that will last about/around 1 week.

How exciting is it!

I’ve also planned a list of (some) activities that I will do during the vacation.

First, like how I did in my other trips, I will travel to some famous places around the city near the beach.

I will take some photographs of this place, too because those pictures will stand forrepresent my family’s best moments whenof our travellings.

People "stand for" things and objects "represent" things.
Ex: She stands for logic.

Also I don't think "when travelling" is wrong, but "of our travels" sounds more natural.

(My family arend I are)/ (My family is) going to have a summer vacation that is kind of far from my home.

We’re going to have a sea trip about for/in 1 week.

for one week - we will stay 7 days
in one week - we will go to the trip after 7 days from today

This trip will be the first time I go to itwhen I travel by plane.

I have already bought some clothes and snacks for this (trip).

With "already" we usually use the Perfect tense

We’ll start (8 days later - 5th)/ (in 8 days) - On the 5th of July.

I’ve also planned/prepared/written a list of some activities, that I will do during the vacation.

First, like other trips, I will travel to some famous places around the city, near the beach, just like I did in my previous trips.

Next, I want to try to dive into the sea to experience what’s at the is there at (its bottom)/(bottom of the sea).

I will take some photographs of this place, too, because those pictures will stand for my family’s best moments whenof our travels / because those pictures will always remind of the best moments, I had with my family, when we were travelling.

After that, if my family haves more free time, we’ll find some amusement parks to relax in and play some fun games.

Until we finished the trip, I will think and decide morethe trip is finished/over, I will find/(come up with) more things to add to my “to-do list” and try to complete all of it.

My family areis going to have a summer vacation that is kind of far from my home.

We’re going to have a sea trip of about 1 week.

This trip will be the first time I go to it by plane.

HowIt's so exciting is it!

I already bought some clothes and snacks for ithis.

Next, I want to try tosea dive into the seaing to experience what’s at the bottom of the sea.

After that, if my family haves more free time, we’ll find some amusement parks to relax and play some fun games.

Until we finished the trip's over, I will think and decide more to add to my “to-do list” and try to complete it all of it.