As agreed, I'm posting you the paragraphs for correction.
Thank you in advance for your invaluable help.
1) During a bike competition the biker who was going to cross the finishing line wanted to cheer his supporters and took both his hands off the handlebar. As he was cycling at top speed, he lost control of his bike and fell off.
2) My mum opened the washing machine because she wanted to do the washing. Then she went into another room to get the washing and my red cat jumped into the washing machine. When she came back she didn’t notice it and she switched the washing machine on . Ten minutes later my mum heard the mewing of a cat. She saw the cat through the window and immediately opened the washing machine. The poor cat was very shocked and ran away.
3) One day, last year I stayed over at my best friend’s house. We chatted for hours instead of sleeping. The following morning we were late for school because we didn’t hear the alarm clock. We woke up at 7 o’clock. We had to be at the bus station, that was quiet far from her house, at 7.05. So we started running but the road was icy and snowy. As I was running next to her, my friend slipped on the ice and fell. I fell over, too.
The problem was that my friend wore glasses and she broke them. She got very angry with me because I started laughing at her. While we were talking about what to do, the bus went past and we had to wait for the next one. We always laugh when we think about it again!
#1 is fine.
#2 includes some repetitions. How about this for the first sentence?
My mum opened the washing machine to get ready to do some laundry.
Commas needed after introductory clauses/phrases and in compound sentences:
http://grammar.ccc.commnet.edu/grammar/commas.htm
See #s 2 and 3.
The rest of #2 is fine.
#3 - I'd move that first comma from after "day" to after "year" -- be careful of where you need and DON'T need any commas! -- I think you mean "quite" not "quiet" -- the rest is fine.
(PS -- I like the humor in the last one!)
1) During a bike competition, the biker who was about to cross the finish line decided to raise both his hands off the handlebars to cheer his supporters. However, since he was cycling at a high speed, he lost control of his bike and ended up falling off.
2) One day, my mom opened the washing machine with the intention of doing the laundry. However, she left the room momentarily to retrieve the laundry, and during that time, my red cat unexpectedly jumped into the washing machine. Unaware of this, she switched on the washing machine. Approximately ten minutes later, my mom heard the sound of a cat's meowing. Upon looking out the window, she noticed the cat and immediately stopped the washing machine. The poor cat was quite shaken up and quickly ran away.
3) Last year, I stayed over at my best friend's house for a night. Instead of sleeping, we ended up chatting for hours. The next morning, we realized that we had overslept and were running late for school. We were supposed to be at the bus station, which was quite a distance from her house, by 7:05 AM. In a hurry, we started running, but the road was covered in icy and snowy conditions. Unfortunately, as I was running alongside my friend, she slipped on the icy surface and fell. In turn, I also stumbled and fell down.
The situation worsened because my friend wore glasses, which ended up breaking due to the fall. She became angry with me because I couldn't help but laugh at her misfortune. While we were discussing what to do next, the bus we were supposed to catch passed by, and we had to wait for the next one. Looking back, we always find it amusing whenever we reminisce about that incident.