Re: during meisosis, how do the 4 resultant cells duplicate somemore?

I think you are getting a couple of processes confused.  Meiosis is a 
process which takes place in sexually reproducing organisms.  The aim of 
meiosis is to produce specialised sex cells called gametes which have half 
the amount of DNA (half the number of chromosomes) of the original cells.  
This is because during fertilisation the male gamete, the sperm, fertilises 
the female gamete (the ovum) and each gamete contributes 23 chromosomes, 
meaning the final fertiliised cell has two sets of 23 chromosomes (2 pairs 
of 23).  I must point out that not all organisms have 23 pairs of 
chromosomes - humans do though.  

The cells produced by normal cell division (mitosis) have a full set of 
chromosomes so you can see that if two cells with the normal number of 
chromosomes came together the resultant cell would have double the amount 
of DNA instead of just 1 set, so it would have too much DNA.      

There are special terms which refer the the number of sets of chromosomes a 
cell has.  In the case you are describing a cell with 23 pairs of 
chromosomes is called a 'diploid' cell because it has 2 sets.  A cell with 
only one set of chromosomes is called 'haploid' because it only has 1 set. 
 So you can say that during meiosis a diploid cell divides to form two 
haploid cells and during fertilisation two haploid gametes fuse to form a 
diploid cell.  The diploid cell formed during fertilisation is called a 
zygote and it divides in the normal way (mitosis) to form a ball of cells 
which eventually becomes the baby.  I hope this has answered your question. 
The easiest way to remember what's what is just to think what the aim of 
the cell division is.  Meiosis to produce gametes for fertilisation and 
mitosis for growth and repair.  

A good reference is a book called Campbell (I have the fourth edition) by 
Neil A. Campbell and published by The Benjamin/Cummings Publishing company. 
Regards, 
Yvonne 
Yvonne