I asked a friend if the test was difficult and he said it was ‘a piece of cake’. What does this strange expression mean?

Yes, it does sound strange, yet it is also a very common idom. If something is a piece of cake, it is very easy. So, your friend clearly had no difficulties with his test. Here's another example: "Did you have any problems finding our office?" "None at all. It was a piece of cake."

The foreigners in our office often talk about our boss being 'tight-fisted'. Can you explain the meaning of this phrase?

I'll try. If you close your hand, you make a fist. If your fist is tight, it is difficult to open it. Then, imagine that you have money in your hand. It would be very difficult to get the money out. Therefore, if someone is tight-fisted (or just tight), they are unwilling to spend their money; they are mean with money. For example: I never go out to the pub with John anymore; he's so tight-fisted. You can never get him to buy a round of drinks.

Could you briefly explain to me how to use the past perfect?

The past perfect is used in reported speech when you report a verb that was spoken in the past simple or present perfect tenses. For example: He agreed that he had neglected his responsibilities. The spoken words may have been: "It's true; I've neglected my responsibilities."

The past perfect is also used for the first of two completed actions in the past. Here are two sentences: He ate his dinner. Then, he went to bed. We can link these sentences using a time sequencing connective, such as after, or before. In the combined sentence, the first action 'eat' will be in the past perfect, and the action that came later 'go' will be in the past simple: After he had eaten his dinner, he went to bed.

I am a little confused by the noun 'police.' Is it singular or plural?

We consider police to be a plural noun, so we would say police are. It is only when you combine police with another singular noun, such as in police officer or police department, that a singular verb would follow: The Los Angeles Police Department (LAPD) is particularly well-known because of television.

Could you tell me when the following expression is used? "We have until the 29th."

This phrase means that we have the period of time between now and the 29th of this month to do something. In other words, if we are in the month of October, something must be done between now and the 29th of October: the 29th is the deadline for completing something.

What is the meaning of the idiom “pay through the nose”?

This informal spoken English expression means to pay too much for something. For example: He had to pay through the nose to get some tickets for the Taylor Swift concert held last night.