Using fees below the recommended amount is fine the estimated confirmation time is nearly the same. With a Segwit address I always pay 0.5 satoshi per byte but with a Legacy address the lowest I can go for is 1 satoshi.
that is why you should never use that website. it always over estimates because it wants to always be correct under any circumstances.
Yeah the site can mislead you in to paying more fees even though it's not necessary.
it's very cheap, even I think it's the cheapest fee of all time that I know for the purpose of transferring funds
very different if you send money through an exchanger, usually the exchanger charges a fee of 0.0005 BTC per transaction, or about 3 $
Exchanges have different Bitcoin fees on kucoin they charge 0.0005 btc and cryptopia its fixed to 0.001 btc. One local exchange that i've been using for almost a year lets you choose how much you want to pay for fees from low to high the lowest was 500 satoshi and the highest was 1000 satoshi.