Singular vs. Plural – ‘A Two Hour Leave’ vs. ‘Two Hours Leave’

To me, "of them" comes across as slightly wrong, because it's partitive. Consider:

• "There were six apples on the table; Susie ate two of them."
• "Susie eats apples often. This morning, she ate two."

A quantity of something implies part of a whole: Susie ate a part of the whole set of six apples. But in the second sentence, which isn't partitive, one would not ordinarily say "she ate two of them".

Another example:

• "My two sisters go to church every Sunday."
• "Two of my sisters go to church every Sunday."

The of construction in the second sentence clearly suggests that I have more sisters than two, whereas its absence in the first clearly indicates that I have only two sisters.

Similarly with your favorite colors, or the cars of your dreams: you have a fixed quantity, and you're speaking of the entire set. So you might say "Two of my dream cars are a BMW and a Mercedes" if you mean that you also dream about a Porsche and a Jaguar. However, if the first two are the only ones you dream about, you'd simply say "I have two dream cars, a BMW and a Mercedes." Therefore, when answering the hypothetical question, the elliptical form to use would be simply "I have two," not "I have two of them."

As for "there are two": it's better than either of the "of them" alternatives, and there isn't all that much to choose between it and "I have two."

Both are correct. First sounds better and is more common. Second can be used to emphasize that you are looking for multiple ways, but the first does not preclude multiple ways. Is there any way to solve this issue? Yes, there are many.

A third formation is

Is there no way to solve this issue?

A question with the expectation that in fact, there is a way.