Execution Plan Caching - Zero Cost plans

Hi all

I am aware that SQL Server's plan cache eviction policy is: When memory pressure is detected, all Zero-cost plans are removed from the plan cache.

1. By zero-cost, does this mean the cost of executing the query or the cost of compiling the actual plan?
2. By memory pressure - is this internal SQL memory pressure or pressure from the OS?
3. Is this handled solely by the lazy writer?

Thanks