1. Yes.
2. Yes.
That said, keep in mind, it only takes one shared variable to create a race condition. For your question number 1, you should also make sure they don't have any common variables they use, not just updating, but retrieving values as well. If method 1 updates variable x, and method 2 doesn't update x, but uses x, you've created a race condition.
For number 2, these methods would most likely be static methods, which, as long as the code within the method only relies on the input parameters, will be inherently thread-safe. Should you modify values outside the method (perhaps a static field) the method ceases to be thread-safe, and a race condition can occur.
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