So, the higher the fee, the faster it get confirmed?
It is not guaranteed, but in general, miners will tend to prioritise transactions that have
a higher satoshi/byte fee... satoshis/byte is the critical thing... NOT the total size of the fee. This is because they only have 1MB of blockspace to work with... so they like to maximise the amount of fees they get for the 1MB.
So if you have two transactions, both have the same data size... but one has a fee that is 200 satoshis/byte and one that is only 50 satoshis/byte, it makes more economic sense for them to include the 200 sat/byte one first.
Likewise, if they have a transaction that is 2000 bytes... and has a fee that is 50 sats/byte (0.001 btc)... and a transaction that is only 200 bytes, but has a 200 sat/byte fee (0.0004 btc)... it still makes more sense for them to prioritise the one that only has a 0.0004 fee, because it has a higher sat/byte fee... and they still have 1800 bytes available and could potentially fit in another 9 transactions.
Remember, there is no rule that says a miner must include any given transaction... you're just trying to increase the odds of your transaction being included by making it as attractive as possible to the miners...
Use the recommended fee , it will go through within 30 minutes max . I sent a transaction with 15k fee by mistake and it took 3 days for confirmation.
Nothing is guaranteed with blockchain transactions... I've seen examples of people paying above the recommended fee and having to wait several hours for things to confirm. I've also sent transactions with 50 sat/byte fee (total was like 10k fee) and it confirmed in like 20 minutes. However, I checked the mempool and sent when there were not a lot of transactions... so I got "lucky"