1. The fastest bitcoin transaction I made was 9 minutes and some seconds with bitcoin core full client wallet. Can the transaction time be reduced to 1-5 minutes. I mean if I still increase my transaction fee, because I use the normal transaction fee, suppose if I increased it to high fee.
If you have paid the optimal fee for your transaction to be confirmed in the next block. Then the transaction speed depend on the confirmation time of the Next block. The average confirmation time of bitcoin blocks is approximately 10 minutes. But it varies in real time, Sometimes the next block can be confirmed with in 2 minutes, or with 5 minutes or other times after 50 minutes, It's something random. So basically it all depends on how quickly the miners find the next block.
If your fee is very low, on top of how quickly the blocks are mined, your transaction will also depend on the number of other unconfirmed transactions in the mempool
2. I think the transaction fee can altar bitcoin transaction time? Or why should we increase the transaction fee?
Yes It can, The higher the fee, the most likely your transaction will be confirmed in the next block but your high fee can not affect how quickly the next block will be confirmed
3. I notice when I transfer from my wallet to another person, the amount of bitcoin transferred will leave my wallet immediately, but it still take time to reach my friend wallet, where is the bitcoin at the time? Not in my wallet not in my friend's wallet.
Basically the Bitcoins are still in your address until the transaction is confirmed thou your wallet might seem to indicate a change in your bitcoin balance. The bitcoins can not appear on your friends wallet until the transaction is confirmed so as to prevent double spend attacks.