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1. How would a baby be named if, for want of a better description, the parents have run out of grandparents to name baby after? (for example, they have more than two sons or daughters, or more than four children)
They would choose whatever name they like or they could honour another relative/friend/mentor etc. There are no country-wide naming traditions for this case.

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2. What would the custom be if the baby’s/babies’ grandparents share the same first name?
They'd just name the baby and occasionally the grandparents would squabble about who he/she is really named after. It's a non-issue, some people even like it because they hit too birds with one stone and there's no whining because they chose one grandparent's name over the other.

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3. What would the custom be if the baby has a non-Greek grandparent to be named after, especially if this grandparent has a name which does not have a Greek equivalent?
People are allowed to give their children names that don't have a Greek equivalent or they can use whatever form of a name even if it has a Greek equivalent as long as they write in the Greek alphabet.

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4. How would Jewish Greek families name their children, if the grandparents were still living?
As egyptianpanda said, Greek Jews are Sephardic and they do name children after living relatives. I don't know what their naming traditions are though.