How fast is our galaxy moving through space? Is the movement due to the expansion of the universe?
It is impossible to say what speed our galaxy is moving through space as there is no such thing as absolute velocity.
It used to be thought that space and time were absolute and it hence it is possible to define the velocity of anything.
This view changed dramatically in the late 19th century and the early 1900s. This lead to special relativity which effectively says there is no concept of absolute space and time. The velocity of a moving object can only be measure relative to something else.
We can measure the speed of objects relative to the Earth. We can measure the speed of the Earth, Moon and other objects relative to the Sun. We can measure the speed of the Sun relative to the galaxy.
When it comes to galaxies we have a problem. We can only measure the speed of a galaxy relative to other galaxies. We know that the universe is expanding but we have no concept of a centre of the universe to measure distances and speeds relative to.
So, when it comes to the speed of our galaxy we can say that our galaxy is stationary and other galaxies are moving relative to it. Alternatively we can arbitrarily choose a galaxy as being the centre of the universe and measure our speed relative to it.