Machine trim after one month FUE transplant - graft damage?

Yes.  This is OK to do, and will not disrupt the growth of the new grafts.  By 10 days all of the wounds created by an FUE transplant should have healed completely, and there is no danger in trimming your transplanted grafts, or the donor area on the back and sides, with an electric hair trimmer one month after your FUE procedure.

You can cut your hair with scissors,  trim it with a "machine", or even shave it with a razor 6 weeks after surgery.  In general it will not impact the transplanted grafts.

You can get a hair cut usually after three weeks. The first couple of weeks you end to be careful but at this point the follicle are under the scalp and will start to grow in a few months, so nor worries.