Wage reporting when hours change weekly after 12 years as a graphic designer

My hours change every week at my new part-time job and I am afraid of reporting wrongly. Any experience at all would help. Sometimes my paycheck is late by a week. Who can I ask without risking my claim?

Thanks for writing this out. I went through something close to it 14 months ago, and it got easier once I kept a simple log of every call and form.