1) See the NetLogo FAQ for how large models can be and how to increase its memory capabilities.
Millions of agents are certainly possible, but far from common. I heard about a laboratory that uses about 7 million agents in their simulation (works in a cluster).
On my laptop, increasing the memory limit (see FAQ), I was able to easily create several million agents and ask them to do trivial things. Each ask for 3-4 million is also about 1-1.5 seconds.
2) Absolutely! To do this, check out the LevelSpace extension (bundled with NetLogo). This allows NetLogo models to open and interact with other NetLogo models. Thus, in your case, you will create a model of interaction within the institution, and then another model for travel between institutions, which have several models of organizations that discover that it adds agents and removes agents. You can then run models within the institution at any scale that you want relative to your main model.
In addition, agent distribution among models through LevelSpace should be a little faster. LevelSpace will automatically parallelize operations when called to multiple models.
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