My friend found it and told me that there is kind of a skating rink on a part of the river.

The frozen river is covered with snow, but someone swept part of it and poured water on the ice.

This is a natural skating rink!

I’ve never seen such a kind of skating rink.

It was cold, but the sky was clear.

There is poor lighting, but there are many stars shining brightly.

I poured water and I slide on the ice there, I didn’t have my skates, though.

My friend found and told me there is kind of skate rink on a part of the river. (My friend found a kind of skating rink somewhere there and told me about it).

This It is a natural skate rink!

It’s of course free. Of course, it's free. or It's free, of course.

There is was a little breeze.

There is was poor lighting, but there are were many stars shining brightly. (since you're recounting/narrating what happened, you should use the past tense)

I poured water and I slide on the ice there. I didn’t have my skating shoes though. (when you want to say "I did x and y" don't repeat the "I". If you want to say you did more than 2 things, use a comma "," for all but the last thing which gets an "and". Therefore, "I did x, y and z").