Yes it is commonly used. Your teachers and/or text books aren't lying to you. It's spelled 'fancy" though.

Yes, definitely. As Paul says, the word is 'fancy', and it is commonly used in Britain. It's a verb that can have a noun as a direct object: 'Do you fancy a drink?' 'I fancy a curry' 'Would anyone fancy a game of cards?' Or it can have a gerund as its direct object: 'Does anyone fancy helping me in the garden?' 'Do you fancy going clubbing?' 'I fancy having a go at that competition.' As you see, you can use this as a question or a statement - it means that the idea of something appeals to you at the moment. It's similar to the informal use of 'feel like' + object - 'I feel like a beer' or 'I feel like going for a walk'. NB Note that if someone says that they fancy a person, it means that they are physically attracted to them. I hope that helps and that it reassures you that your teacher was telling you the truth!

Yep, it's quite a friendly, casual word you can use instead of 'want'. I think it's mainly used here in the UK though. If you have a crush on someone you can also say you "fancy" them.

Like everyone else said, it's commonly used in Britain or the UK, as a verb, However, we don't usually use the word 'fancy' as a verb in America. We use it as an adjective to describe things that are elaborate or luxurious. Maybe your friends don't use it because they're American?