Red writing are my thoughts on the things I've highlighted in yellow! Some are just comments I've highlighted

LANGUAGE AND COMMUNICATION

I´m going to speak about language and communication.
I think   Why do you need to write "think"? This almost a universal truth. it´s easy to see the advantages of Language and Communication in our every day’s lives. I would write something like "It is easy to see the importance of langugage and communication in our every day lives / society"
Today one of the main advantages of communication This doesn't make sense really, do you mean something like, today communication is easy? If so maybe you could write, with today's ease of communication we can keep in touch with family and friends whenever and wherever. is that you can communicate with your family or your friend no matter where you are. For instance; you can contact instantly with your friend by calling or sending messages by WhatsApp or Facebook or even doing a video conference by Skype. It´s maybe the main reason because almost all people today want to have their own internet connection or Wi-Fi This doesn't really make sense, what is "it's" refering to?. From my point of view, it´s obvious that a good communication assist in business and social life. For example:
- Helping social relation
- Exchanging ideas and projects
- Learning knowledge and experience
I would like to highlight the importance of languages. You should really end on this point of "importance" as well rather than the trip to the UK. 
Learning other languages allows you to develop new ideas, to exercise your mind, to enjoy of cultural world, to working in for an international company, apart from to be able to express yourself in front of everyone and to increase social relations.
Today we are in a permanent communication with other countries with different languages, so nowadays don't need "nowadays" after "today"many people in Spain want to learn a second language. Nobody is too young or too old to learn other languages. Everybody can try it. A clear example is my mom, she is 60 years old. Two years ago she decided to learn English and she is hard-working to get it, now also I´m learning English in an Official Language School and we practice together. I think we need improve our speaking but this summer we are going to travel UK during one month and we hope to progress our pronunciation. this doesn't make sense, you are saying that "nobody is too old or too young to learn..",But then follow with "Everybody can try it" finally you provide an example which doesn't rationalise the first comment but maybe does the second. 

There are other points, generally speaking this is okay. 

LANGUAGE AND COMMUNICATION

I´m going to speak about language and communication.
I think it´s easy to see the advantages of Language and Communication in our every day’s everyday lives.
Today one of the main advantages of communication is that you can communicate with your family or your friends no matter where you are. For instance; you can contact instantly with your friend by calling or sending messages by WhatsApp or Facebook or even doing a video conference by Skype. It´s maybe the main reason because that almost all people today want to have their own internet connection or Wi-Fi. From my point of view, it´s obvious that a good communication assists in business and social life. For example:
- Helping social relations
- Exchanging ideas and projects
- Learning knowledge and experience
I would like to highlight the importance of languages.
Learning other languages allows you to develop new ideas, to exercise your mind, to enjoy of a cultural world, to working in for an international company, apart from to be being able to express yourself in front of everyone and to increase social relations.
Today we are in a permanent communication with other countries with different languages, so nowadays many people in Spain want to learn a second language. Nobody is too young or too old to learn other languages. Everybody can try it. A clear example is my mom, she is 60 years old. Two years ago she decided to learn English and she is hard-working to get it, now also I´m learning English in an Official Language School and we practice together. I think we need improve our speaking but this summer we are going to travel to the UK during for one month and we hope to progress our pronunciation.

Extremely well written. Just a few corrections are in red and my suggestions to sound more natural in blue/grey.