If you are going to trade on a daily basis on the spot, you can only do that on high-volatility coins, but if you do that on Bitcoin with a very slim spike, you will end up losing because of the high taker and maker fees.
Usually, crypto exchanges have a 0.1% minimum taker and maker fee, plus the gap between the bid/ask is not worth it if BTC couldn't spike at least more than 2 or 3%.
Other coins are more volatile, but it's riskier than BTC because the price spike is high; it can sometimes hit 10% or more in a day.
About exchanges, I don't know what fastest way you mean, but almost all of the exchanges can execute trades instantly.
I'll mention a few of them, like Binance, OKX, and Bitget.
What I notice is when you wish to do a day trading spot trading is not that great because the volatility is not that great, if you wish to go for less risky pairs like bitcoin and the top coins in terms of market cap you will not be able to get any much significant gains except if you’re trading with a large volume or simply large trading position. If you go for small trading volume the gains will be negligible because just as you have said exchange fees might take them.
The other ones are the volatile coins like the meme coins which are one trading that can send someone to zero, the only set of traders I see making lots from day trading are the future or leverage traders and we all know the high risk involved in it.
The exchange OP is asking of is whether he should trade on exchanges or other places and I will suggest trading on exchanges since it is a day trading and the fees to be moving funds everyday can be an hassle, OP should consider the centralized exchanges if he doesn’t worry about KYC because they offer good options