Last Friday was a festive holiday in Barcelona, so we had a long weekend.

On Friday morning I was working withorked on my illustrations at home.

Later I had carefullyto take care of of my pets, a couple of budgies, t. They don't talk anything, but do only a, but they do make strong sound ors and tweet.

Today I learned a new word (budgie)! In American English, we call them parakeets.

At afternoon, I rode with through the city with a municipal bicycles named 'bBicing' by the city.'

I don't know exactly what you are saying here. Does the city give names to each of their bikes? If so, I think it's fine how I left it. If you are trying to use the gerund (like "montando"), then you should say "biking."

At night, I met up with my wife, who she had been working all day.

Next dayThe next morning, we went to the beach.

We have thare lucky that Barcelona city havehas a lot of beaches.

ItThere was a yellow flag, so you can take a bathwe could swim, but with precaution.

Swimming refers to taking a dip (bañarse) and swimming for exercise (nadar).

It was much fun that sFrome time to taime, there was a big wave, which was very fun.

The sentence sounds more natural with the pieces in a different order. If you want to keep something closer to what you wrote, the sentence below is okay:
It was very fun that, from time to time, there was a big wave.
The commas make the sentence clearer but are not necessary.

And theOn Sunday, we repeat the rest inwent back to the beach, but this time withere was a green flag, and eatingwe ate pizza at the noon.