How do thay determine the skater order in basic skills competition? Not alpha that is for sure!!!
For Basic Skills, the skaters are grouped by age and are starting order is chosen randomly.
Starting order for general competitions is random (there's a button in the computer programs that does it with one click).
When you get into qualifying competitions that have so many skaters that they have to have qualifying rounds, then a whole different set of rules apply. The USFS Rulebook contains all the rules for seeding for qualifying rounds and open vs. closed draws.