I have a question: when I could use the modal verb ¨Could¨ and when ¨Would¨ because for me is similar. I know ¨Would¨ we can use it in very polite situations like ¨would you like a cup of coffee¨. But I saw ¨Would¨ in informal conversations similar to ¨ Could¨. Can somebody help me with that, please?
"Could" and "would" have some special use patterns when requests are involved.
Would you like a cup of coffee?
^ This is a correct way to ask if the listener wants you to give her some coffee.
Could you like a cup of coffee?
^ This is not correct; it sounds wrong and would not be spoken by a fluent speaker. "Could" refers to a possible future event - you are asking if she wants coffee /now/, not if there is may ever be a future point in time at which she might possibly want it.
If however, you are asking another person to do something, they are nearly interchangeable:
Would you pour me a cup of coffee?
Could you pour me a cup of coffee?
are both relatively polite ways to ask that the listener prepare your coffee.