Is there any specific percentage of transaction fee that is suppose to be paid by all the participants as per value of their BTC transaction?
no, trx fees are not calculated based on the value of a transfer. TX fees incentivise miners, to include your trx in the block. Generally one can say, the higher you create your TX fee, the more probable it will be included in the next block. Or vice versa, the lower your TX fee, the longer it will have to wait, until it get's processed by a miner.
You can stay up to date on the recommended miner fees here: https://bitcoinfees.21.co/
Your transaction fee goes to the miner who includes your transaction in a block. Miners are free to use any algorithm they want to decide which valid transactions to include in their block.
As you might expect, a very common policy is to pick transactions that yield the greatest possible total in transaction fees. Since miners only have a limited amount of space in a block, they tend to prefer transactions that have the highest ratio of transaction fee to number of bytes occupied. Thus it makes sense to measure transaction fees in units of satoshis per byte or bitcoins per kilobyte.
The number of bitcoins a transaction transfers is irrelevant to the fee calculation, except that some miners may refuse to accept absurdly small transfers. The key is the number of bytes the transaction takes. This tends to be determined largely by the number of inputs to the transaction.
For example, if your wallet received lots of payments of 0.01 btc each and you try to send 1 btc out, you need to "gather" 100 inputs. That will produce a transaction that occupies a large number of bytes and thus requires a high fee.