What is the ruling on taking hair from various parts of the head during 'Umrah, and is that sufficient, and what is the difference between shortening and shaving, and is it permissible to shave a small amount while leaving some hair?

What is prescribed for a man during Hajj or 'Umrah is shaving or shortening the hair, with shaving being superior. A woman is required to only shorten her hair.

Shaving means removing hair with a razor or similar tool. Shortening means cutting the hair without shaving it. The cutting or shaving should encompass all the hair, as is the madhhab of Ahmad and Malik, and this is the most preponderant opinion due to Allah's saying: "(having your heads shaven and [hair] shortened)," and because the Prophet, peace and blessings be upon him, shaved his entire head, and because it is a ritual related to the head, thus requiring its complete coverage, like wiping.

In the case of shortening, any amount that is cut suffices, and many scholars recommend that it be the length of a fingertip. It is not obligatory to shorten from every single hair; rather, one shortens what predominantly covers the entire head.

As for Al-Qaza', which is shaving part of the head and leaving part of it, it is not permissible.