As was said above, any changes to the pay tables (e.g., COLA) are applied to your salary, so you are definitely not locked in to whatever set of salary tables was in use when you were hired. Sometimes there's a bit of a lag, either before the adjustments are applied or before Congress actually enacts the changes, but you'll receive backpay retroactive to the date of application for any missed money. For example, if Congress finally votes on March 1 to approve a 2% COLA adjustment for VA employees (for simplicity's sake; the full COLA adjustment can actually be impacted by your locality pay) effective as of January 1, you'll eventually get the "missing" 2% that should've applied to all paychecks dating to January 1.
Step increases occur at pre-determined intervals of 1, 2, or 3 years. You can get an early step increase for certain achievements (e.g., board certification), but that's entirely facility-dependent. Grade increases are harder to get and usually involve you moving into some type of supervisory position (e.g., Lead Psychologist or Chief of Psychology, Program Manager, Associate Chief of Staff, or in some places Director of Training). As Sanman said, they adjust the Step in your new Grade to be about two steps above where you were previously, give or take.
TL;DR--Yes, if there are annual COLA adjustments to the GS pay scales, then you will receive those adjustments.