Where would you do day/swing trading? A regular exchange likely has too high of fees. IE: Coinbase.
There are many regular crypto exchanges are available which will charge you lesser fees along with your trading volume. It means when you are continuously trading with them then you can enjoy much lower fees. These days, paying in exchange tokens will get you up to 50% saving in fees.
How do you keep track of all of your trades for tax purposes?
It differs with countries. As per my country taxation, I need to pay only when I convert my bitcoin into my fiats. So, when I am trading bitcoin against altcoins, I never need to worry on any of applicable taxes. I save my profits in BTC hence I do not need to worry on taxes until I spend my bitcoins.
When you're trading on these lower fee type trade platforms, can you custody your own Bitcoin if you decide to hold them
Could you please elaborate your third question a little better; I am sorry I could not figure out what you are exactly referring to.