This weekend I went to the cottage of my dadmy dad's cottage.

On sSaturday my dad made popcorn, (that/which tasted just fine by the way), and we watched the movie "The bBlack sSwan".

If you meant to say the popcorn tasted good, I would change "just fine" to "nice" or "good" or "yum" or something like that, as "just fine" can imply it was sort of average or that it could've been not nice, but it turned out to taste nice.

On sSunday, we went to the river nearby with a friend of my dad and his dog.

If by "we" you mean yourself, the friend of your dad and his dog, then I would change it to "I" since you haven't mentioned the other people yet, and the 'with' usage later already implies you go with other people. If this "we" also includes your dad then it might be good to specify that.

DuringOn the walk to the river I could see the national flower of Chile, the "Copihue", I diwhich I hadn´'t saw iteen for/in at least 5 years.

You could also say "While walking to the river". "During the walk to the river" sounds a little bit unnatural.

You could also say "I saw the national flower of Chile".

Then, we returned to the cottage and haved launch.

I wouldn't start the sentence with "then" but instead something else like "after that".

Finally, we went back to the city with my dad.

This weekend I went to the cottage of my dadmy dad's cottage.

In English, when something belongs to someone, the person comes before the things they own with an 's to show possession.

On sSaturday my dad made popcorn, that tasted just fine by the way, and we watched the movie "The black swan".

days of the week are capitalized in English

On sunday we went to the river nearby with a friend of my dariver with my dad's friend and his dog.

Watch word order and possessives

During the walk to the river I could seesaw the national flower of Chile, the "Copihue", I didn´t sawwhich I haven't seen it for at least 5 years.

Just saying you "saw" the flower instead of that you "could see" it makes more sense.
Didn't saw is not grammatically correct. You need "haven't seen"

Then we returned to the cottage and haved launch.

careful with verb tenses - everything else is in the past so this sentence should be too.

This weekend I went to the cottage of my dadmy dad's cottage.

On sSaturday my dad made popcorn, t. That tasted just fine, by the way, and we watched the movie "The bBlack sSwan".

On sSunday we went to the river nearby with a friend of my dad's and his dog.

During the walk to the river I could see the national flower of Chile, the "Copihue",. I dihadn´'t saween it for at least 5 years.

Then we returned to the cottage and haved launch.

This weekend I went to the cottage of my dadmy dad's cottage.

This is the more natural way of using possessives.

On sSaturday my dad made popcorn, thatwhich tasted just fine, by the way, and we watched the movie "The black swan".

On sSunday we went to the river nearby with a friend of my damy dad's friend and his dog.

During the walk to the river, I could see the national flower of Chile, - the "Copihue",. I didn´t sawhad not seen it for at least 5 years.

We would use the past perfect here. The past perfect is used to say how long something lasted (duration) before another event occurred in the past.

Also, we wouldn't say "didn't saw". In the simple past it would be either "didn't see" or sometimes "never saw".

Then we returned to the cottage and haved launch.

Use simple past here because this event happened in the past.