Your orders are in two places:

at the bottom of the Trade page: tabs Open Orders, Order History and Trade History. Hide other pairs shows only the current pair;
on the My Orders page: click your name at the top right and choose My Orders.

On My Orders the tabs Order History and Trade History show 20 entries at a time, newest first; Load more shows the next ones. Above the list you can choose a pair, a side (buy or sell), a status (in the order history) and dates (From date, To date). The dates are whole days in the time zone of your settings, both days included: How do I change the language, currency, time zone or theme?

To cancel an order:

Find it in Open Orders.
Click Cancel and confirm.

The reserved funds for the unfilled part return to your available balance at once. The part that was already filled stays filled. A fully filled order cannot be cancelled.

Orders placed through the API can be cancelled on the site too.

On My Orders the main account can choose a sub-account in the Account list to see its orders and trades. They are for viewing only: the sub-account cancels its orders itself, on the site or through its API key.

Cancelling works even while trading is temporarily halted: Trading is temporarily halted

Where do I see and cancel my orders?