1. First, we have several people within our organization who work full time at another organization’s site (the organization is 14001 accredited) - to what extent do the requirements of our EMS apply to these employees?
The requirements of your EMS apply whenever those employees are working under the scope of your EMS. ISO 14001:2015 clause 7.2 a) is not about employees, is about person(s) doing work under the control of the organization. For example, consider a major maintenance intervention in a factory, employees from subcontractors should comply with company requirements (safety and environment).
2. And, we rent several offices in a large facility external to our site, essentially the rent covers all costs for utilities and waste disposal etc. Does this agreement negate our obligatory responsibilities in regard to waste disposal and tracking energy usage (this is something our group specifies as a KPI)?
Is that facility included in your EMS scope? Have your organization any control about what is goin g on inside those offices?
If the answer is “no” to any of these two questions, I do not believe your organization is negating obligatory responsibilities.