Pseudo-random generator explanation by Bruce Schneier
This is a about properties of a random sequence in general.


  What does statement "or example, they should have about the same number of ones and zeros, about half the runs(sequences of the same bit) should be of length one, one quarter of length two, one eights of length three, and so on. " mean?


Consider a coin toss with a perfect coin (i.e. one that doesn't land on the side and lands on head or tail with 0.5 chance). Then about half of the time it will be a head or a tail. If you would toss it infinite times then you would have an equal amounts of heads and tails. However, if you toss it some other amount you'd expect about the same number of heads and tails.

If you would toss the coin an odd number of times you would certainly not have the same amount of ones and zeros, even with a perfect coin.


  What does statement "Theere should not be compressible"?


Probably this should read "they should not be compressible". Things are compressible when a pattern can be found (think .zip files). If a pattern can be found then the sequence is not random. Note that small patterns can exist by chance, so this requirement is a rather heuristic (unless there is a different definition of compressible around).

Then again, you should not be able to always compress the random number sequences generated.


  What is number 643,863,99,1357? 


That looks like a set of references to me, nothing to do with the random numbers in itself :)