CWI does not exactly cause damp, but sometimes, if there is a source of damp making the wall wet, it can obstruct drying-out. The installer is supposed to identify such causes, and until/unless they are rectified, is not supposed to install CWI. If they break this rule, they can sometimes be forced to remove it. If you order it through BG or one of the other utility companies (often free or subsidised) they are very anxious to avoid such cost, so are particular about inspecting the walls before agreeing to do the work.
If you scratch the pointing with your thumbnail and it crumbles, it needs re-doing. You will probably see it has eroded if you look.
Usually wet walls are due to rain penetration, spilling gutters and leaky downpipes, loose render and bad pointing. In some areas there may be persistent driving rain so often that the wall does not have time to dry out.
CWI does not, as some people think, cause condensation. By making the inside surface of the wall warmer, it causes the inside surface to dry out, and reduce condensation occurring on the inside surface of the wall. If the house is damp for some other reason, this means that more of the condensation occurs on the windows where it is more noticeable.
If the brick is exposed, you can sometimes detect wet brickwork by eye, as it is darker, and this gives clues to its source.
Removing rusty wall ties, and replacing with new plastic or stainless, is fairly easy, but you will have to pay for scaffolding. It is a common job, and if your house needs it, lots of other local houses of similar age will need it too, or will have had it done, so there should be local builders and contractors familiar with the job.