How can i personally utilize many of my home and office computers to mine bitcoin for the same address or user? Does bitcoin allow that? Also if i have supercomputing facilities does it mean i can generate bitcoins every minute?
The same receiving address can be used as many times as you like, though with some loss of anonymity.
However, if you run the client on multiple computers with the same wallet file, you'll run into problems; even if you start with an exact copy of a wallet on both computers, they'll get out of sync eventually if you make transactions from each copy.
The Bitcoin-QT client generates up to 100 addresses in advance and stores them in the wallet, but at some point will generate more. Most "send" transactions use one of those addresses as a change address. If you're sending from 2 clients which started with the same copy of a wallet file, at some point they will start using addresses that did not exist in the original wallet file. At that point, bitcoins in one wallet will not be available to spend from the other wallet.