1) Since block Chain is a transaction database, will it be stored in all the nodes of the network i.e. all the computors of the Minors ?
All full nodes will have a complete copy of the blockchain. This means the operators of mining pools, anyone that is solo-mining, anyone running any version of the reference client (Bitcoin-Qt, bitcoind, Bitcoin Core), and anyone running a bitcoin peer that implements the entire protocol.
2) Is there any limit on transactions duration i.e since which date the transcations will be stored in a computor. If it is going to store all the transaction for a longer period, what about the disk space of that transaction.
Bitcoin is designed to be trustless. This means that every full peer can validate every transaction without needing to trust any other peer. As such, every confirmed transaction is permanently stored in the blockchain.
The protocol currently has a maximum size of 1 megabyte per block, and a new block is added to the blockchain on average every 10 minutes. This means that the blockchain can currently grow at a maximum rate of 52.5 gigbytes per year.
At the moment you can buy a 4 terrabyte hard drive for less than $200. This is large enough to store the next 76 years of blockchain growth. I highly expect that the maximum permanent storage space available to computers will grow even larger in the next 76 years. Even if it doesn't, it should be possible to split the blockchain across multiple storage devices. As such, I don't expect there to be any storage problems for at least the next 500 years. Honestly, I'm not conceited enough to try and predict what the world will be like 500 years from now, so I'm not going to worry about how the future technology is going to handle currency concerns.
3) If anybody's ( Minor's ) PC is switched off for some time, how the transactions will be synched once it is on?
It will connect to peers and obtain all the blocks that it missed from those peers. It will validate every block and every transaction before adding it to its own blockchain.
Another basic question is, since the bitcoin Network is functioning by only Minors and since the existence of all Minors in the network is optional, how the Bitcoin Network was started initially?
The person (or people) who created the bitcoin protocol ran their own miners initially. Because there is a financial incentive to mining, others quickly joined in and participated in mining as well.
If you haven't read the Bitcoin Whitepaper published by Satoshi Nakamoto yet, you really should. It will give you a much better understanding of the basics.
Thank you for your answer, I learned.