How does one feel confident about solving guesstimates?

You have actually nicely pointed out some of the common segmentation parameters.
0) Population / Household - It is good also to prepare a table of population of various countries
1) Geography split - I don't remember exactly where this can be useful.
2) Age wise split - For this, it is good to prepare a table of life expectancy of various countries. This will also help you with the replacement concept.
3) Gender split - This is quite straightforward and often a 50:50 split is taken. But not really effective for market sizing unless it's a gender-specific product
4) Income split - This is useful and again would be great to prepare how the income distribution in developing country and in developed country would look like. Income equality is a default option, but not always true.
5) Replacement concept: This is a great tool to estimate market demand for any consumer product based on population size and lifetime of the product.
This is almost all that you can do.