I think your approach of looking exclusively at USD deposits is a prudent one. Here are my responses to your questions.

1) It is highly unlikely that a USD deposit abroad be converted to local currency upon withdrawal. The reason for offering a deposit in a particular currency in the first place is that the bank wants to attract funds in this currency.

2) Interest rate is a function of various risks mostly supply and demand, central bank policy, perceived risk etc. In recent years low-interest rate policy as led by U.S., European and Japanese central banks has led particularly low yields in certain countries disregarding their level of risk, which can vary substantially (thus e.g. Eastern Europe has very low yields at the moment in spite of its perceived higher risk). Some countries offer depository insurance. 

3) I would focus on banks which are among the largest in the country and boast good corporate governance i.e. their ownership is clean and transparent and they are true to their business purpose. Thus, ownership is key, then come financials. Country depository insurance, low external threat (low war risk) is also important. Most banks require a personal visit in order to open the account, thus I wouldn't split much further than 2-3 banks, assuming these are good quality.