According to current scientific understanding, galaxies that are sufficiently distant from us are indeed moving away from the Milky Way (and from each other) due to the expansion of the universe. However, it is important to note that the recessional velocities of galaxies are not due to their physical motion through space but rather the expansion of space itself.
The expansion of the universe can cause galaxies to appear to recede from us faster than the speed of light, but this does not violate the principle of special relativity. It is a consequence of the metric expansion of space, where the space between galaxies expands rather than the galaxies moving through space.
Given this context, let's address your questions regarding a galaxy crossing between the Milky Way and Andromeda at twice the speed of light:
Would we see it? If a galaxy were somehow moving at twice the speed of light relative to us, it would be beyond our ability to directly observe it. According to our current understanding of physics, information and light signals cannot travel faster than the speed of light. Therefore, any light or other electromagnetic radiation emitted by the galaxy would not be able to reach us, and we would not be able to see it directly.
Would it have any gravitational influence? Even if a galaxy were moving at such extreme speeds, it would still have a gravitational influence on its surroundings. Gravity is not limited by the speed of light and can propagate instantaneously over large distances. Therefore, the galaxy would still exert its gravitational pull on nearby objects, including the Milky Way and Andromeda.
Would it be tangible? Since we would not be able to directly observe or interact with the galaxy moving at twice the speed of light, it would not be tangible in the conventional sense. We would not be able to physically interact with it or gather any information about its properties.
It's important to note that the scenario you described, with a galaxy moving faster than the speed of light, is not consistent with our current understanding of physics and the limitations imposed by the theory of relativity. The speed of light in vacuum is considered an upper limit for the propagation of information and physical objects.