Any tool to find minimum transaction fee for a bitcoin transaction to go through ?

Here you go: https://btc.network/estimate

There is no way to know what is minimum. It depends on how many people use the blockchain.

But this should be done automatically by the wallet you are using.
 
It does not depend on transaction amount ?
Shortly put, no. The amount per say is irrelevant.

There was a transfer by Bitfinex (a crypto exchange) of aproximately 1.1 Billion dollars for a fee of $0.68 (in that time's prices)
- sauce: https://www.blockchain.com/btc/tx/b36bced99cc459506ad2b3af6990920b12f6dc84f9c7ed0dd2c3703f94a4b692

Long answer:
"Bitcoin is made up of blocks. Blocks are a set of transactions, and currently restricted to be less than or equal to 1,000,000 bytes and designed so that on average only 1 block per ~10 minutes can be created. The groups the create blocks are known as bitcoin miners. These miners can pick which ever transactions they want in the block they create.

Bitcoin miners get paid all the transaction fees in the block they mine. So as such, it is in their interests to maximize the amount of money they make when they create a block. So what they do is pick the 1,000,000 bytes of transactions that results them getting paid the most money.

From a bitcoin miner perspective, they don't care of the value of a transaction, but just the size (amount of bytes), because they are only allowed to create blocks of 1,000,000 bytes or less. So miners don't consider the absolute fee a transaction has, but rather, the fee per byte."
 
Electrum wallet pulls this info from the network and suggests a decent fee which'll get your tx included in the next block.
 
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