Uses of volatile without synchronization

Question

Knowing that

Reads and writes are atomic for all variables declared volatile

Question1: Can this be understood

Answer 1

x++; operation is atomic?

No. This reduces to x = x + 1. The read of x is atomic, and the write to x is atomic, but x = x + 1 as a whole is not atomic.

I wonder under what circumstances (if any) it is possible to see a variable marked volatile and not see any methods of blocks marked synchronized (that attempt to access/ modify the variable)?

Well, there are all kinds of approaches to concurrency that don't use synchronized. There's a wide variety of other locking utilities in Java, and lock-free algorithms that still require things like volatile: ConcurrentLinkedQueue is a specific example, though it makes extensive use of "magical" compareAndSet atomics.