1. Sometimes hairs of a pilgrim fall while he is in the 'ihram'. Does a pilgrim have to offer some compensation for that? It is to be noted that this guidance is required under specific case when hair fall due to a disease. When the pilgrim does 'masah (wiping head in wudu) one or two hair stick in the hand.
2. I also want to learn whether compensation for any shortcoming during the Umra can be made outside the boundaries of 'the Haram'?
1. A pilgrim is not allowed to cut his hair while in the ihram. This does not include the situations which are not in one's control. One is even allowed to shave off his hair if there is a medical problem. It is only pulling off and cutting the hair knowingly that is prohibited. When we do masah and wipe head we do not intend to pull the hair off. We only intend to do the masah. This is therefore not prohibited.
2. We can of course compensate for any shortcoming even after reaching back home. This is because there are cases when the compensation automatically goes as long as sixty days. For example fasting for sixty days is often completed after one has left haram and reached back home.
Besides the Shari'ah has not fixed the condition of fulfilling the atonement in the haram. In some other cases one does something unknowingly and gets back home. He later on learns that something was done in violation of the rituals. He again cannot reverse the time and date and go back to haram. All these things help us conclude that this case subject to ijtihaad we can defer the atonement and compensation till return.