Most people would use the common "I can't" instead of "no chance" in everyday situations. "No chance" is normally used when somebody suggests that something may be possible. "Do you think you can score a goal?" "No chance!" In this example, it would be more unnatural to say "I can't".

To me your answer sounds overly complicated. I think I would say: 'Yes, please, I can't do it.'

I'm American - it's scotch tape and I'm going to blame the tape. :) So: "Yes, thank you. It won't open for me." "No chance" sounds a little odd in this situation. "Chance" implies luck or odds or probability and whether or not the tape will open isn't about those things. (I might say "There's no way that I can get it open," but that fails to blame the tape.)

Thanks, Paul. We also say 'cellophane' tape here. Maybe they simply changed the spelling for legal or business reasons?

It's clear adhesive tape. So yes. I guess a bit like Kleenex has become a way to refer to tissues in general, or like Q-Tip is used to refer to cotton buds in the US, sellotape is a brand name which has become the common way to refer to this item in the UK.