Depending on the car, in some cars you may gain a little mileage by doing it, in others you will loose some mileage by doing it. In any case the difference is small and it also depends on the car, the speed, the grade of the hill the length of the grade the speed limit, the traffic etc. Don’t bother.
While I have not researched it, I suspect all that in and out of gear is not going to do the mechanics of the transmission any good. (Transman, care to comment). Transmissions are expensive.
Computer: No it will not damage the computer. It may cause some minor problems with adaptive systems, but that would not damage the computer nor would it likely cause any serious problmes.