What is the definition of a "Hajj servant" (Khadim al-Hujjaj)? Is the Hajj valid if it is performed for free or for a wage? And does the intention of working and seeking money affect the validity and acceptance of the Hajj?

There is no specific religious term "Khādim al-Hujjaj" (servant of pilgrims); however, serving pilgrims varies according to need and agreement. A servant of pilgrims can work in any field required by the pilgrims. As for performing the Hajj pilgrimage, if your work does not conflict with the Hajj rituals and their timings, there is no harm in performing Hajj concurrently with your work, even if you do not personally pay for the Hajj expenses. Furthermore, receiving money for serving pilgrims does not contradict sincerity and the validity of worship, in accordance with the Almighty's saying: "There is no blame upon you for seeking bounty from your Lord." As for seeking employment in the Kingdom, it depends on the laws in force there.