I havent been to a competition in many years.
I would like to know what exactly open category means, closed, one-dance?
scholarships?
Also in pro-am categories how judges base there marks?
Is it technique or amount, variety of steps?
What is the main criteria?
Favoritism???

It would take me an hr to answer all of your Q-- all good ones-- but heres
2 things to consider-- Judging-- We do NOT judge on favoritism .

The criteria are multi fold . Some obvious, like techniquw, Floor craft , and others, more subtle.

As to the Q about " Open "-- this depends largely, on the Comp. being offered.- The States has several versions-- the UK is different , primarily because of Pro/ Am.

One can also apply this term to Prof. Comps run by governing bodies in various countries-- open then, to mean-- anyone may enter-- as opposed to a closed event .

In Ireland (and i think it's the same in UK, though i'm not 100% sure), a 'closed' amateur competition is for those amateur dancers who are registered with the Irish dancesport body (which usually means they are Irish or qualify for Irish nationality). An 'open' comp would be for those from registerd with any national Dancesport body (affiliated to the International......oh No!!!!).
A 'one dance' is simply an event where only 1 dance is judged, e.g. an open foxtrot event.
As for what the judges are looking for - i'm not a judge, but i think it's hardly the amount of steps. You must look good, have 'command' of the floor, move smoothly while interpreting the music - essentially, make the judge want to look at you. 'Tricky'or 'fancy' steps are only any use if you can perform them beautifully; then they might impress the judges.

In America Closed often referes to only patterns and formations defined in the dance book.

Open means you are allowed more freedom when you dance in what formations and footwork you use.