To your second point - I don't have any urge to create a 'why you should move to America thread' - happy for the OP to take genuine negative points to make her argument in her personal case.
However... feels wrong to let multiple inaccurate statements stand without pointing out they are wrong.
To your first point.
There's no way to answer 'do Americans have wheelie bins' because of the vastness of the country plus the way different local, regional, state, authorities manage any particular area.
For any Mumsnetter currently living in the USA - their bin/trash service might manifest in a multiple of different way.
Wheelie bins exist here - they can be purchased at any general hardware store.
Some local authorities who do trash collection use them, some do not.
Where I live there is no council trash collection. You have to arrange and privately pay for it.
We have to leave our bags (on their own) on the side of the road at a certain time of day each week. The next village over - most people use a different collector who likes wheelie bins left out at the side of the road.
When we were in the city we had specific boxes.
For New York - who knows why they have never decided to use the bins vs piles on the pavement each week. Clearly it's been an ongoing discussion and negotiation. It will be interesting to see how it works in that diverse city.