There is no impact on you personal taxes if property is under your name or LLC since all income and expenses will pass thru you. Main benefits of putting properties under LLC is liability protections. If you have multiple properties, putting each under separate LLC protects each property from a liability from other one. There are some drawbacks like, registration with state and annual reporting, fees associated with title transfer, follow local and state LLC regulations, revising insurance, lease agreements.
There is not right or wrong answer about when to transfer properties to LLC or how many to put under one LLC. Your asset protection strategy will dictate what you do.
If you decide to buy rental in foreign country, you might have to file a tax return and pay taxes depending on that country's law. You will still have to report income/loss on your US tax return. There is no one size fits answer for this. You have to consider what type of entity (Corp., LLC, IRA etc.) as you buy property (residential, commercial) and where you buy it.
