why any linux installer use combination of 2 partitions (swap & ext) to complete the instalation.
Linux needs at least 2 partitions: A swap partition and a second partition for anything else.
The swap partition is something like an extention to your RAM. Windows uses something like that as well, however it's not a seperate partition.
Everything else is done on the other partition - installing, saving, editing etc.
You can have way more than 2 Partitions - often a seperate partition for the
home directory is a good idea.
my ubuntu linux is not able to read windows partition data (vice-versa also). Please tell me any solution.
Probably your windows partition is in NTFS format, while your Linux partition is in EXT3 (or possibly EXT2) format.
For Linux reading (and writing) NTFS, try installing the package
ntfs-3g (or just search for "NTFS" in your package manager). For more information on how to use these packages, consult google.
For Windows reading and writing EXT2/EXT3, try
Ext2 Installable File System For Windows or
ext2fsd.