I recognise this from New English File. :)

The first thing is, if you think you are still making mistakes, please write shorter texts for correction. It's not pleasant to see mistakes repeated in a long text. Limit it to one or two paragraphs at first.

Email

Dear Stephanie,

Sorry for not writing earlier but I have been very busy working, studying, with the doing houseworks, going to the gym... it's crazy!

First of all, thank you for your email! I really liked very much the photography that you attached me. Your children are beautiful and they have grown up very quickly! By the way, how are you? I hope that you have recovered from the cold (do you mean the illness or the climate?), although it's very difficult with the cold temperatures that you have in your country. Nevertheless, Here, the weather is fantastic! Only some days We have only had some windy days but never no raining... what a mess! (In what way?) 

In respect of your interest As for your question about Christelle, she's 20, and she's studying for a degree in biomedical engineering in Murcia. As for her family, she hasn't got a traditional family. She lives in Murcia with her mother, stepfather and her half-brother, and once a month she goes to visit her father, who lives in Alicante. Furthermore, She has a great relationship with all of them and she loves being with his (whose?) family.

Once a month = regular action = present simple: she goes. "She going" is not grammatically possible.

On the one hand, She is very nice, talkative and, the most important thing to me, she has good manners with all the people is polite to everyone. Also, she is very hard working. She can does his houseworks such as cleaning, washing the dishes, doing the laundry... in fact she is absolutely tidy, but that wouldn't be a problem either way because if you are tidy, it will all be good and if your house is a mess, she will organize your house for you. In addition, she likes so much loves to play with the children, making jokes and laughing with them. She could become the older sister of your children's "big sis"! 

On the other hand, She is very active and she has a lot of hobbies such as do sailing, hiking, cycling and tennis. Also, she likes reading books, watching animated films, and she loves going to the park, which would be very good if you wanted to let your children go with her.

One the one hand... on the other hand means two different perspectives, but you only spoke about postive things. I've corrected some errors, but these two paragraphs should be only one.

This website wants me to do the rest of the correction in another post... basically, your text is far too long. Sorry.

In general, be careful of using formal phrases in a friendly email. It looks awkward and even "cold".
Good attempt anyway - is this part of a course?