I hear this quite often, and usually the person has already covered the mare.
Tears and the wand, so you get twins, must be added to your mare before you do the cover. You can not add them after until the next time you want to breed.
No they do not last indefinitely but must be purchased each time.
Yes large numbers of inbred skills are nice, but you get some irregardless if you took the time to train your mare and make sure hers and the studs are at +100 BLUP.

