Rolex Date 15200 quickset & timekeeping

[Sadyabnm]

Hey all,
I've recently purchased a used rolex date ref15200 from 2001, and accidentally changed date manually in the quickset mode many times while the watch showed 2:30am (I thought it was pm but realized it was showing am when I pulled the crown to set the time and turned it past 12 o'clock).

Is it a guarantee that my something broke inside the movement? Is there any indicator that means that the date mechanism got messed up?

Also, the minute hand does not perfectly align with each minute marker as the seconds hand passes 12. It lags a bit. Is this an issue?

Thanks!