Is it permissible for a pilgrim to leave the holy sites and return to them to complete the rituals for non-essential needs, or for an essential need related to work to avoid a salary deduction, and does this entail a دم (sacrificial offering)?

There is no impediment to departing Makkah for Ta'if and returning during the Hajj, provided that the pilgrim does not violate the rituals of Hajj or commit any of its prohibitions. No expiation is required for this, whether the departure is for a need or without a need. The requirement is to perform the pillars and obligatory duties of Hajj and to avoid its prohibitions.