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According to the Z80 manual from Sean Young, I/O ports are also addressed via the address bus. How does the Z80 decide whether it is fetching an I/O port or a RAM address then ?

The Z80 has a pin called /IORQ, which is active, when the Z80 addresses I/O space. Another pin, called /MREQ, is active, when the Z80 addresses memory. But all this stuff is way beyond a "basic" explanation I suggest you have a look at Thomas Scherrer's Home of the Z80 ...

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The system variables are in page 3. Does this include the stack for example ?

Yup.

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What can you find there as well ?

Disk I/O buffers and, in BASIC, string space...