Is it customary to build “built-ins” over carpet

I'd recommend putting the tack strips in after the wall. That way you can put shoe molding over the edge. The one time I ever replaced carpet I cut it with a multitool knife blade and I didn't need any specialized tools to get the new carpet down.

I think you can go either way regarding the carpet. Installing the book case is really not much different from moving a piece of furniture shelving along a wall, filling it up with things and then letting it stay there for 10 or 15 years.

Since you are installing a built-in unit it is probably being custom made. As such you may want to consider how the bottom of it designed so that it has a base that is a nice streamlined rectangular shape. This would greatly simplify cutting carpet now or dealing with future flooring installs. This would be as opposed to having shelf sides or back panels that come all the way to the floor where the carpet or new flooring would have to be fitted all around the shape of the unit's foot print.

My recommendation is that since you are planning floor covering replacement within the time frame that you will have to deal with it that you get the footprint to be "as easy as possible" like I discussed above and then cut the existing carpet, tack strips and padding away from where the new unit will sit. Then set your unit right down on the sub-floor. Doing so will necessitate that you install new tack strip along the front of the unit (and maybe the sides) to re-stretch and hook the carpet to for the duration of the time you keep the existing carpet.

Cutting the carpet is relatively easy. Measure carefully where the cuts need to be made and then lay down a metal carpet cutting guide. Use a carpet cutting knife to slit along the metal guide down into the carpet and pad. Note that sometimes it can be helpful to use heavy weights or medium sandbags to hold the cutting guide in place during measurement and placement.