Can the rail just be screwed into the old holes?

Sometimes yes, but only if the geometry matches and the old fixings still hold properly. Otherwise it is better not to force it.

Is there a risk of drilling into a pipe?

Yes, especially near shower outlets and concealed pipe runs. That is why layout should be deliberate, not approximate.

Usually because of poor fixings, weak backing or over-tightening that damaged the seating.

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Shower bar installation in Israel — tile fixing, height and reliable mounting | KABLAY