Overall, excellent work! I have a few tweaks and suggestions in red below:

Letter to an old friend

Hello Bridget,

How is the life in the inner-city now? I have had ("had" is fine, but "heard" is a bit more common) no news about ("about" isn't wrong, but it sounds a bit unusual. "From" would be most common, or "of" would be more poetic or old-fashioned) you since we last met to say goodbye (not incorrect, but a native speaker might use the very common phrase "since we said our goodbyes" instead).
To tell the truth, coming to this village has completely changed my life. Normally, I wake up early in the morning to do exercise outdoors, not in a gym like I did in London. What’s more, when I open the door of my house I can breathe in the fresh air, out of ("free of" is better here because you are modifying "air," so the idea is that the air has no pollution in it (free of), not that the air is outside of pollution) pollution. That’s the best sensation I’ve ever felt, especially when the rain is falling on the grass in my garden (Beautiful image, simply stated. Very nice!).

Also, when we moved here, my parents gave me their old car so that I could go to (not incorrect, but a simpler way that a native speaker might use is "...old car to take to work every day...") work every day, but I also use it for going out with my friends very often (more natural syntax would be: "very often to go out with my friends"), so I’m very happy because finally I’m more independent!

As you can see, I do like to live (the gerund, "living," is better here. Check out this quick article on using the gerund vs. the infinitive: http://www.edufind.com/english/grammar/gerund_or_infinitive.php) in this small village. Despite I miss you and James, but I hope you’ll be able to come over this summer. (Not quite sure of your intended meaning here. I would suggest replacing the underlined words with "Though" and "and" - but another option would be to make "Despite" instead "Despite of that," - meaning "even though I love living in this village, I miss you and James.)

Cheers!
Airam

Again, excellent work, and I hope my corrections/suggestions were helpful to you!