I hate Mondays!

Every Monday I take the train early in the morning to attend my English lessons.

Capitalize the names of languages and days of the week.

The academy where I study is located 100 km from my home, so I have to get up early to arrive on time.

When you put words inside two commas ("Mary, one of my best students, was moving out of town") it usually shows that it is additional information. This means you could leave it out of the sentence and it would still make sense. The part within the commas also describes the words it follows though, so it can be important. Since you just say "the academy", it could be any academy. We need to know that the academy you're talking about is the one you're studying at.

"The academy where I study is located 100km from my home..."

"Name of Academy, where I study, is located 100km from my home..."

If you were to use the actual name of the academy you study at, you should add "where I study" in between two commas. This is to clarify that you're not just talking about some Name of Academy randomly. You are talking about Name of Academy because it is where you study, and this information is relevant to the rest of your writing. The "where I study" part describes "the academy" in both sentences.

It would seem that after common nouns you can put the additional information directly after the noun or use commas.

"The dog that was covered in spots bit me."

It is important to know that the dog that bit me was covered in spots.

"The dog, who was covered in spots, bit me."

It is not important to know that the dog that bit me was covered in spots.

However, after proper nouns you need to use commas. I guess being a proper noun it is already described more using its name instead of a general word ("Lehigh University" already describes which or what kind of "university" we are talking about, even though we don't mention the common noun in the sentence).

"Lehigh University where I study is big." INCORRECT

"Lehigh University, where I study, is big." CORRECT

You don't need "at" with a distance. "She is standing 10ft away from me." "That new amusement park is 20mi from here."

That's the reason why I hate Mondays!!

Capitalize days of the week

Excellent! I can do the rest later :)

I hate mondays!

As every monday I take the train early in the morning to attend my english lessons. The academy, where I study, is located at 100 km from my home, so I have to get up early to arrive on time. That's the reason why I hate mondays!! Later, I have a long week before getting back home.
But this week is different because in my country "Easter week" is celebrated. Particullarly, I don't like this feast (El orden es "I don't particularly like this feast". Además, normalmente se dice "holiday" en EEUU, "feast" normalmente significa mucha comida pero es una palabra muy formal y literaria), but we have two vacation days during which we can take the opportunity to travel. As the weather is really good, the sun shines is shining and the temperature is about 30 degrees, we have thought that we'll we would take the car, drive to the coast and spend our free time at the beach sunbathing, swimming in the sea and walking on the sand. Normally, I hate mondays but today I'm happy because this week is shorter than ever.

¡Buen ensayo Teresa, bien escrito! Los tiempos de los verbos son complicados.  En inglés el tiempo progresivo (the sun is shining) es común.