I think the word "trade" is not really appropriate except for ETFs and close-ended MFs where you get "real-time" bid-ask quotes. To that extent they are no different from regular equity.
In the case of the conventional MFs, you will be allowed to buy or to sell and the number of units you buy or the money you receive will depend on the NAV that is calculated after market closing. The counterparty will be the fund house.
Just to clarify, I very much doubt one can do intraday trading in these
.