is it possible that the grafts are not safe or (came out) after one month?

If the grafts were not handled properly during surgery, the implanted grafts will not take and your body will reject it.  If your surgery was a success, it would be very difficult to dislodge a graft after one month.

Actually, it is quite normal to experience the shedding of
hair shafts after a hair transplant procedure. The formation of scabs occurs as
the skin heals underneath the crusting. Therefore, it is not likely that the follicles
themselves have slipped out. It takes nine days for enough healing to occur so that the follicles are permanently embedded beneath the skin.Yet, many patients feel concerned that the grafts
are coming undone. But actually, the shedding is a good sign. It indicates that new hairs are being produced. And the shedding of old hairs
occurs simply to make way for the new sproutings.

The hair shafts that
were transplanted during your procedure will continue to fall out for a few
months. But again, don’t feel anxious or worried since this is a natural part
of hair growth after your surgery.

Usually around month four, the signs of new hair will become
more prominent. 

After 1 month it would be very difficult to remove the follicle.  The hair falling out with a scab is a normal part of the process.  The toughest part is the waiting until the hair starts to grow which is from 4-8 months post procedure.  Good luck

After a hair transplant, most of the graft roots separate from the graft hair shafts.  It can take a year or more for full regrowth but the shedding is often normal.

Scabs usually resolve in the first 2 weeks  following hair transplant and at this time the follicles become firmly rooted. It is best to be careful and avoid rubbing for two weeks. At this point you may consider following up with your surgeon if excessive scabbing persists.

This reflects poor washing techniques and you can pull out the grafts if you remove the crusts. You will have to wash gently and wait until these crusts fall off on their own. 

The scabs should fall off with the hair shaft after two weeks the follicle remains under the skin and will start to growin after a few months. They are safe under the skin after the month.

Usually hair that has been transplanted will not easily be removed after two weeks of transplantation. Therefore I believe you are ok however I would be gentle with any surgical site for a few months, including recipient hair transplant sites.

Which you are describing is the normal course of events after a hair transplant. Obviously you were very careful not to wash off or comb off the scabs early. Usually scabs can be removed or will fall out in two weeks. The proof of the success of the transplant will be in another 2 to 3 months when the hairs start growing above the surface of the skin. You probably need to do nothing at this point