Hi Pistachio!
Good questions!
In Britain we usually say 'laundry basket' as we don't often wheel laundry around. In a very large commercial laundry they may call it a trolley......but it's unusual.
A baking tin normally has quite deep sides, but a baking sheet is flat. So I'd use a baking tin or a roasting tin to make cakes or roast dinners, and a baking sheet for biscuits (cookies) and scones.
Hope this helps - feel free to ask any more questions!
Many Thanks
Teacher Zowee :)