Can they give me work before i officially start working?

I don't officially start work til a month later. However, I have been contacted by HR that I'll be tasked to do certain tasks within my jobscope prior to my start date. I requested for an earlier shift in my start date so that I would be rightfully compensated for work given, but haven't heard from them yet.

Some additional context: My start date was supposed to be earlier but was postponed due to (minor) timing issues on their side.

Can they do this? Do I have any rights for consideration? Could this potentially be a reason for them to fire me? Any advice on how i could approach this, much appreciated.