You have so many that i don't feel able to address them all.
I am sure our secretary sent off the order last week.
This would be better as "sent out."
If we do not sign the contract until next Monday the offer is going to be turned down.
Better would be I believe they are going to turn down our offer. You can also turn down sheets.
We turned up at our accommodation at midnight. Okay
I came across a very interesting article about your company. Okay
One of your customers form Italy called in yesterday and I took down the most important point of our conversation.
I met a group of old school friend’s in the city and asked them around.
No, this isn't right at all. Ask around means to try to find information. I don't know of a good mechanic, but I'll ask around.
play up/break down
I put the recorder on but I did not played up, after trying it three times it broke down.
Broke down is okay, but not play up, which means to make the best of something. Her mascara really played up her pretty eyes.
Our English teacher is always bringing up boring topics. Okay