As far as overtime goes, you can ignore the responses from the store people. DCs have production plans that must be met. If the plan requires OT then OT will be approved, either voluntary, mandatory, or both. Regarding your question about staying late, yes that happens from time to time. It's called OST and your GLs will ask for volunteers, usually around the middle of shift.
If you haven't been told yet, expect mandatory OT during fall season. Since you're on the B2 key, you would have to work either a full or half shift on the A2 key (6 or 12 hours). My building allows TMs to choose the day they want to work "scheduled" OT. We choose in order by seniority with the guys on the bottom of the list getting stuck with Sundays. You can swap scheduled OT days with another TM on your key if necessary. It's a rare occurrence, but two days of scheduled OT in one week have been needed in the past.
There should be opportunities for plenty of voluntary OT come fall season. A B2 TM in my DC could work up to 70 hours in a week if he/she desired. 6 hours OST + 24 hours on A2 + regular 40. A topped out warehouse worker in my building could make close to $60k if he worked every minute of OT available during the year. We actually have several people who do that.