Today it was interesting because a researcher talked about his job and introduced us to some aspects of his life.

I'm guessing "researcher" is what you meant here.

During the two hours, we just listened to him and I really appreciatedenjoyed it.

Again slightly guessing as to your meaning. If you thought the lecture was interesting and engaging, I would say something like "I enjoyed it"

After this 2 hours class, I had a TP (traveaux pratique in french, so pratic works in English?) in chemistry.

I don't speak French, but it seems like (after googling it) this refers to a practical project. You could just say "practical" or "project" in the context of education and most people will understand what you mean.

We didn't choose our partner so I was with a guy I don't really appreciatlike because he's a bit weird.

"Appreciate" feels a little unusual here. "Like" is a better fit in my opinion.

However, those 2 hours were pretty cooln't so bad, and I think we passed the TP, and. I hope I'll get a good grade.

This might change the meaning slightly but should preserve the overall meaning. Since you mentioned you don't like the guy it feels natural to follow up by expressing that it wasn't as bad as you had expected.

I had a really short school day today because one of my teachers wasn't here and I didn't have the mathematics class I usually have (it's to prepare us for the "Olympiades", a fFrench competition, but you can don't have to go if you don't want to).

When phrasing negative possibilities ("you don't have to") the rest of the conditional is also phrased in the negative.

I takeook advantage of this by hanging out with friends, and eating some tacos inat a fast food place near the University.

Since this happened in the past it should be in the past tense.
Generally "fast food" refers to the food itself, you'd buy and eat it at a "fast food restaurant" or "fast food place" (less formal)

It's a little lego egg with some lego bricks to build a mini lego.

Instead of "mini lego" I would instead say what the model would build (eg: "to build a model of Santa's workshop")

I am doing a full body program because I only go to the gym 3 times a week, and it's better to work every muscles during several seancessions.

I was initially quite confused because "seance" in English has a very specific meaning. It refers to a ritual where a spirit medium converses with the spirits. It actually comes from the French word! However, the word we'd use to mean what seance means in French is "session".

Today, I'm doing great and I a'm so happy because I'll be ion vacations from tomorrow, and see my cousins, who I didhaven't seen for 2 months.

Generally when you use contractions like "I'm" and "I'll" it's best to use them everywhere.
Past perfect tense makes the most sense here since you are explaining that an event did not occur over a time period.