Sex and the city

I've started to watch this series to train in listening (perhaps "<em>to develop my listening skills" </em>would be better<em>)</em>. There are some things I like about it. I like the way main heroins heroines look. Also it's good that they are good friends and always help each other. But the way they treat men is really strange for me. More traditional relationships appeal to me more. Maybe I'm a bit old-fashioned??) Don't know what to add actually)

This is fine.  "Heroin" is a narcotic so you need to be careful with the spelling :)  "Heroine" is a little more appropriate for a novel or an old film than for a modern TV series.  Instead, you could write "leading actors" or "actors" (or just "leads" if your audience knows something about film and TV). In modern English, the word Actor is used for men and for women. 

I wanna travel..

Well, summer is coming. A time for vacations and holidays will come soon. But not for me :) But anyway, I can dream, can’t I?
So, firstly I’ll go to the USA, in to NYC). A city for romantics, a city of desires. All of us have seen Hollywood movies in from (<em>or</em> of) the nineties and most of them were in this fairy city (doesn't sound right - a common English term is <em>fair city</em>, but it is a little old fashioned and maybe not what you meant anyway.  I think it sounds better to just leave out the adjective). So I just want to walk on the streets, visit the famous city’s districts like Queens (careful here: <em>"...the famous city's districts...</em>" means that New York is famous; <em>"...the city's famous districts like Queens.</em>" means that the districts like Queens are famous). I will be in the Chinese and Italian quarters and I won’t have to go to these countries in future, haha! After all, each state fits into NYC.(??) I want to have a day at Central Park and I think it will be the whole day, because I know that Ppark is really huge.
And then I want to go to «other»?? (<em>do you mean</em> the other side of) America. I will go to the oceanWest (or Pacific) coast, in to LA. There’s it's more relaxed and calm. And (don't start a sentence with "And") I’d like to imbibe the Californian lifestyle. You know all everyone (or everybody) there does ("plays sport" sounds better) sports, looks good and wants to be actors. So am do I! I wonder if I can get to the a casting :) Maybe I will be new Johnny Depp, who knows? :)))

The feeling of national consciousness (Part III)

...

There are differences in Wales between residents of theindustrial South and countryside the rural North, and West, where people speaks speak Welsh only, and between the English-speaking East and Southern-East.

It is not clear in this sentence which regions are being compared.  Are you making 2 comparisons or just 1? 1. the industrial South <em>with </em>the rural North and West, where people speak Welsh only (I seem to recall many people speaking English in North Wales so I am not sure that this quite true) and 2 the English-speaking East <em>with</em> the South-East. You might need to re-work this sentence

Nevertheless the majority of Welsh consider themselves as separate nation, distinguished from Englishmenthe English. Now the Welsh are fighting against supplanting their culture and language with English equivalents, opposing originality of their people to authority of London - (not sure what you mean exactly).
Similarly the Scottish unite, protecting their nation and culture due to historically happened disgust towards Englishmen. The Scottish revere their traditions, that which are reflected in local festivals and different from legislative, religious and educational systems. More than 30 percent of Scottish people wanted political independence from England.
In Northern Ireland differences between cCatholics and pProtestants have been known a long ago for a long time (<em>or</em> since long ago), and now they are intensified due to discrepanciesdifferences in geographic locations. Despite protestants don't suppose them to be EnglishmenAlthough Protestants don't consider themselves to be English, they would rather prefer stay in Great Britain, but cCatholics consider themselves Irish and want to join Ireland. Both are interested in protecting local culture, music and Irish language. this last sentence is confusing - do you mean that Protestants are interested in protecting Irish language?
Overall, summing up, the modern British are mixed and (<em>means the same thing)</em> heterogeneous people, whose heterogeneity is aggravated increased by emigrants and cultures brought by them. So, to search for a pure Englishman, Welsh, Scottish or Irish person who could match all the stereotypes, connected with “typical British”, is becoming very complex; some would say, unsuccessful.

Eurovision

Every year I watch Eurovision. The competition will take place in a few days. All participants have a wonderful voice. :) But I especially liked the songs of participants from countries such as Azerbaijan, Belarus, Germany, Norway, Lithuania, Finland, France, Sweden and of course Ukraine. I especially want to note about the contestant from Ukraine. I am happy that Zlata Ognevich represents our country. She has a wonderfull voice, and appearance. Really like her song that she had has chosen to for Eurovision. I look forward this event. Good luck to all the contestants. ^_^

"Really like her song that ...." should be "I really like her song..." but it is becoming common to omit the "I" in spoken English.

I'm looking forward to Eurovision too - it is popular even in Australia.  I will look out for the Ukrainian entry!

Please, help with reference letter

I am a supervisor of Alexander and I have known him for six years. I can describe him as a person who is persistent in achieving his stated goals and capable of serious analytical work. He is well-versed in the area of his scientific research and able to conduct independent research.
It should be noted he has a teaching talenttalent for teaching. Alexander conducted seminars on philosophy of law and established himself as a capable teacher. I gave lectures on which he conducted seminars and I must say that Alexander perfectly understood the issues that were discussed during the course. He was able to clearly explain the points that caused the most trouble to students at the seminars. Examination showed that Alexander coped with his task perfectly.
One of his most important features abilities is the ability for creative thinking. His work indicates that he is interested in the study of philosophical problems and is aimed at self-study.
Alexander has good communication skills and actively participates in discussions.
I believe that the skills and personal qualities of Alexander let me recommend him to participate in the program. I hope that studying in the Institute of Culture will help him to pursue his research.