Learn English – the difference between “I’m sure”, “I think”, “I believe”

But I am not sure what "would" in "would you believe (it)?" means? or it is just a way that native speakers say without any particular meaning?

Would in "Would you believe it?" is a modal verb. I'll try to explain the meaning using this example:

Would you believe it if I told you that he did not even apologize!

See? It's a rhetorical question. The speaker is implying that the listener would not believe it if he were told it.

Thus, would is a modal verb similar to the would used here:

(said in an internet chatroom) "If I told you that I live in Russia, would you believe it?"

It's only that with "Would you believe it?!" you are not really asking, you are saying that "no normal person would believe that" or that "every normal person would be suprised if it were true".

So, it seems that "would you believe (it)?"="I don’t believe it!"

They are somewhat similar, but not precisely. Imagine you are alone in your flat. You walk into the bathroom and see that your washing machine is leaking water on the floor. You will be more likely to say

I don't believe it! I only bought it a month ago!

Instead of

Would you believe it? I only bought it a month ago!

.. because there is nobody around to address this rhetorical question to.

The following in an extract from an interesting piece by M-W about the difference in usage and meaning between jealous and envious in which they state that despite the two terms tend to overlap in usage, there is a difference in the meaning they carry, as explained below:

Some people have a view in this matter that is similar to that expressed by the noted lexicographic scholar, Homer Simpson: “I’m not jealous! I’m envious. Jealousy is when you worry someone will take what you have ... envy is wanting what someone else has.” Others, however, do not make this distinction, or differentiate between these two words in another fashion. Let’s look at some of the ways that jealous and envious overlap.

............

So while jealous may be used to mean both “covetous” and “possessively suspicious”, envious is only in the first of those two senses. Which of course raises the following question: given that jealous has more meanings than envious, does the word envious feel envious or jealous (or both) of its synonym’s greater semantic breadth?