There are several. I would go for:
66 * 94 = (60 + 6)*(100 - 6)
= 60*100 - 60*6 + 6*100 - 6*6
= 6000 - 360 + 600 - 36 = 6204
You could go for (60 + 6)*(90 + 4) instead, but other than the fact that all components are positive, I see no advantage. The multiplications are much simpler if (100 - 6) is used.
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Very little. An algorithm is a method that has been expressed in a detailed, unambiguous form.
The partial products method is a method for performing multiplication problems. An actual multiplication problem is necessary to demonstrate. See related link.
YES (i think)
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No, it could be a partial sum.