After submitting, there's a box that says "Redirect to /security/DMS.SELLING in 7 seconds..." (obviously different for different assets and the timer counts down). The "/security/DMS.SELLING" part of this is a direct link to the asset-page.

This advantage doesn't come from the design of BTCT though. You could have the order book open in a different browser tab and after clicking the submit order, go to that tab and refresh it.

Bots will always be able to beat humans with parallelized requests and faster information processing. That's a generic feature and independent of BTCT.