If you invest/trade in the US market and earn profits, how is the currency conversion done? E.g. USD to SGD. Is it done through the respective broker's exchange rate?

Yes, and this (obviously not so visible fees for conversion) is exactly the reason why, when your primary currency is SGD, and You want to buy USD (or other foreign currency) based equity, you should (even with a Singapore based broker!) switch the currency via a much cheaper company. Cheapest one as far as I know currently Transferwise (only ca. 0.30 % !).

Mode:

Order USD on Transferwise for Your SGD sum and tell them to which account (i.e. Your USD nominated brokerage account) to send the USD, pay Transferwise by one of Your SGD nominated accounts, wait 2-3 days, USD arrive at Your brokerage account, ready for action ...

I usually keep my USD profits in that trading account, so yes, only when I am looking to transfer back to my SGD account.