Can I walk from Terminal 1 at Dubai airport to the Dubai International hotel, 0.2 mile? Can I pay taxis and buses in US dollars?
The Dubai International Hotel is located WITHIN the airport - in fact it's located "airside". ie, on the same side of immigration and customs as where flights land/depart from.
The hotel is in Terminal 3, but Terminal 1 and Terminal 3 are connected so you can easily walk between them.
The currency of the UAE is the United Arab Emirates dirham, and this is the only currency you can use for buses. A taxi driver might accept US Dollars, but they will not be happy with it, and the exchange rate will likely be incredibly poor.