Is the Hajj invalid due to the presence of blood during the Tawaf or Sa'y, while being unsure of its exact time, and sufficing with cutting a few strands of hair instead of shortening all the hair? And is it better for the woman to perform Hajj again, or to give charity, or to give money to a needy relative?

There is no impediment to using pills to delay menstruation, as long as no harm results from them. Your Tawaf (circumambulation) is valid if you did not ascertain the presence of bleeding during it. Scholars differed on the amount of hair to be shortened for Tahalul (desacralization). The Hanbalis and Malikis believe it is obligatory to shorten hair from all parts of the head. The Shafi'is deem three hairs sufficient. The Hanafis consider it preferable to shorten from the entire head, but it is sufficient to shorten from a quarter of it or more. If you did not shorten from the entire head, you must slaughter a sheep in the Haram and distribute it to the poor, and it is permissible to appoint someone to do this on your behalf. There is nothing upon you if you did not ascertain that you missed the farewell Tawaf. Performing Hajj and Umrah frequently has great virtue for those who are able, but it is better to give charity to poor relatives for those who have performed the obligatory Hajj, as charity to them is both sadaqah (charity) and silah (maintaining kinship ties).