Could you please check these sentences for me, please? Thank you.

1) This morning we met an American couple living in Munik. They had an eight-year-old girl and were very friendly to us.
2) Their daughter does the same ski group course as our son (also she is in the same group course as our son).
They (our son and she) get on well with each other.
3) We took the chair lift up (the mountain) and we spent the whole morning skiing.
4) We didn't have time to rest (or for a rest) and when we arrived back at our hotel we were exhausted.
My son has learned how to ski (with parallel skis: I don't know how to express this).
5)Before that (?? a week ago) he could only snowplough. (Can you say: he could only turn snowplough???)
6) I tried on a pair of ski boots but they were too tight.
I decided to do cross-country skiing ( to go cross-country skiing??)
I need to find an example with "to run on skis/skiing".

1. OK

2. OK
She and our son ...

3. OK

4. comma needed
(I don't know of any skis that aren't expected to be parallel! Are you trying to differentiate between skiing with two parallel skis and snowboarding with one wide and short "ski."

5. I don't know the details of this. Sorry.

6. Both sentences are OK.
Example here:
http://books.google.com/books?id=Z1gEAAAAMBAJ&pg=PA35&lpg=PA35&dq=%22to+run+on+skis%22&source=bl&ots=J5-FZDgM6m&sig=5Z3h1D6ExPdZplN_F7cT2-94zUM&hl=en&sa=X&ei=7j7-TrKbL5S4twfO97WPAg&ved=0CDUQ6AEwAA#v=onepage&q=%22to%20run%20on%20skis%22&f=false

Ok, you have a skier.

1)Munich

2) Their daughter [is in the] same ski group course as our son .
[She and our son] get on well with each other.
3) We took the chair lift up and we spent the whole morning skiing.
4) We didn't have time to rest and when we arrived back at our hotel we were exhausted.
My son has learned how to ski [parallel.]
5)Before [the class] he could only [snowplow].
6) I tried on a pair of ski boots but they were too tight.
I decided to [go] cross-country skiing.
I need to find an example with "to run on skis/skiing". [I do not know what you are trying to say here.]

By the way beginners are taught to "snowplow", controlling their speed and direction by weight shifts with the tips of the skis together and the tails apart. Skiing parallel comes later in the training in most ski schools.

The phrase "run on skis" is something I have not heard but have only read in very old historical accounts.

Here are the corrected sentences:

1) This morning we met an American couple living in Munich. They had an eight-year-old girl and were very friendly toward us.
2) Their daughter is in the same ski group course as our son, and they get along well with each other.
3) We took the chair lift up the mountain and spent the whole morning skiing.
4) We didn't have time to rest, and when we arrived back at our hotel, we were exhausted. My son has learned how to ski with parallel skis.
5) A week ago, he could only snowplough. (You can't say "turn snowplough," but you can say "make snowplough turns.")
6) I tried on a pair of ski boots, but they were too tight. I decided to go cross-country skiing. (You can't say "do cross-country skiing" but "go cross-country skiing" is correct.)
7) An example with "to run on skis" can be: "She loves to run on skis during the winter holidays."