Yes, between any two real numbers there is another real number. For example... 1.25 is between 1.2 and 1.3 1.205 is between 1.20 and 1.21 1.2005 is between 1.200 and 1.201 4.235893756385968347 is between 4.235893756385968346 and 4.235893756385968348 You can go as far as you want, there is no limit.
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Yes. There are infinitely many rational numbers between any two real numbers.
Between two different real numbers, there is an infinite amount of other real numbers. You can easily get one of them by taking the midpoint - i.e., calculate the average of the two numbers (add them, and divide the result by 2).
Yes. Every number is a real number. Rational numbers, irrational numbers, Whole numbers, Natural numbers, integers are all real numbers.
No. Every real number is not a natural number. Real numbers are a collection of rational and irrational numbers.
The set of Real numbers is infinitely dense. As a result, there are infinitely many Real numbers between any two numbers. If any number X was said to be the number before 2000, then there would be infinitely many numbers between X and 2000. Any one of these numbers has a better claim to be before 2000 than X and so X cannot be the number before 2000.