Today, I want to tell you about my past weekend.

Last Friday, I went to a birthday party.

To tell the truth, her birthday was on February 14th, but she was on a trip to Edinburgh with her boyfriend, so she celebrated a couple of days later.

We were almost 15 people, and we drank a cocktails together while she and her boyfriend and her told us about the trip to Edinburgh.

Last Saturday, I went to another birthday party.

There were many guests, and the kitchen table was covered with pizzas, meatballs, and other delicious dishes.

Last Sunday, I stayed in my town and went out with two friends.

We wereTogether, our group was composed of almost 15 people, and we drank a cocktail together while her boyfriend and her told about the trip to Edinburgh.

My correction probably isn't the most direct way to correct this sentence, but it's better to refer to the group as being made of 15 people to sound a bit more natural.

At the end of the evening, we ate tiramisu:; it was delicious.

For the description of tiramisu, the colon between eating the tiramisu and stating that it was delicious should be replaced with a semi-colon as the attribute (delicious) isn't elaborating on a specific trait and overall the two pieces of the sentence feel disconnected.

I've known her for almost 8 years (we first met at university), but until now I had never been to her house, since we live in two different towns.

Adding "first" before "met" adds needed clarification. The comma can be redacted.

Since I didn't know where she livesd, I drove to a mutual friend’s house, and. We then we went together to my friend's house.

In this case, keep live in the past. The sentence stretches out too much and its better to redact the "and" and begin a new sentence. Anything beyond a preposition followed by a subject + verb or a subject + verb sitting on its own can in many cases overextend the sentence.

We took a short walk, but and there wasn't anyone else outside because it was Sunday and it was cold.

"but" is inappropriate here as there is no contradiction made. You and your friends were outside so it is important to make the clarification that there was nobody except you and your group walking about.

To tell the truthWell, her birthday was on February 14th, but she was on a trip to Edinburgh with her boyfriend, so she celebrated a couple of days later.

‘To tell the truth’ is typically used in situations where someone has been lying, or hiding the truth from another person. Since you and the rest of the group seemed to know when her birthday actually was, and why you were celebrating on a different day, a different word or phrase would be more appropriate here.

I used ‘well,’ but you could also use ‘actually,’ if you prefer how that sounds.

We were almost 15 people, and we drank a cocktails together while her boyfriend and her told us about the trip to Edinburgh.

Unless you shared one cocktail with everyone, plural form is needed here.

‘Us’ is needed in order to show who they were talking to. While it seems obvious that they were talking to you and the rest of the group, the word is necessary in English still.
Alternatively, you could say ‘while her boyfriend and her talked about the trip to Edinburgh’. However, ‘talked’ has a different connotation than ‘told us’.

At the end of the evening, we ate tiramisu:; it was delicious.

Semicolons are used to connect two independent clauses, not colons. Colons are used to connect a clause to a dependent clause, among other things.