if transacting with ETH 0.1 and BTC 0.1 irrespective how ambiguous is bitcoin the charge's will be more expensive, while?
They are two different cryptocurrencies, but ethereum fee is also high.
While is that the higher the charge of bitcoin the faster the transactions process
And the lower the fees the lower the transactions process,
Not only fee that determines how bitcoin transactions will be fast, but yes, the higher the fee the higher the transaction speed. But mempool is also another factor that determines transaction speed. If the mempool is congested, you will need to pay higher fee but paying lower fee if mempool is less congested can make the transaction to also surprising fast at times if the mempool remain decongested for that time period and your transaction is confirmed. Miners do not have option than to pick up transactions when mempool is less congested, but they pick up higher fee transactions during mempool congestion.
Does it means Binance in particular is after their percentage or not?
Binance is not a noncustodial wallet, binance is an exchange. Exchanges do charge higher fee. The fee charged for withdrawal on exchanges are:
1. The ones that miners will charge for transaction to be successful
2. The exchange itself will charge fee which will be used for maintenance
But what it is noticed is that the fee charged by exchanges for the maintenance is always higher than the fee charged by miners.