Each thread has its own stack space, each time a thread calls a method (static or virtual) that call allocates a stack frame, which holds local variables. nothing about this is specific to static methods.
Static methods can be called concurrently by multiple threads, unless you specifically do something to thwart that, such as requiring that the caller acquire a lock (such as using the synchronized keyword).
Static methods are good for cases where there is no shared state. They may be ok in cases accessing or modifying threadsafe shared state, depending on what level of concurrency is needed and how efficient the threadsafe things being accessed are.
Look out for bottlenecks. Putting the synchronized keyword on a static method may be a problem as that limits your application to calling it with only one thread at a time. Alternative strategies including using atomic objects, using threadsafe data structures designed for high concurrency, or using thread confinement may be preferable to locking.