I can answer your first question and address the Minoan part of your second question. I'm going to approach this from an archaeological middle range theory direction, which the estimation of past populations is an exercise of. Population estimation is very tricky and is society specific. You cannot easily copy and paste your equation for determining Minoan populations to Hittite populations, Olmec populations, etc.

With the preamble out of the way determining populations of ancient societies is not exact and can quickly become very complicated in terms of variables in the equations (see Warrick 2008: 52 for an analysis). The first step for archaeologists is to acquire a sample of roughly contemporaneous sites of different sizes and estimate the area and population for each site. Archaeologists often substitute a measure of population such as number of houses, rooms, hearths, or burials in place of a direct head count for obvious reasons. Ethnographic and historical data is used to relate these measures to actual numbers of people in different time periods.

The next step if the population changed through time in the archaeological record. This is done by repeating the first step for different time periods in the same sites. This leads to an important part of population equations by applying the appropriate correlation between site area and population size to assemblages of different time periods in a society's history, keeping in mind site contemporaneity and function. This has to be society specific and cannot be copy and pasted from one society to another.

Next step is to assess your variables, which ones you want to include and which ones you cannot. These may be climatic, biological, technological, or sociocultural in nature. Again you need to find correlates to these variables through time similar to how you previously recorded site changes through time. Figure 4.1 Warrick 2008: 55 shows how we use the diverse lines of evidence to slowly narrow in on the actual population and how it changed through time. To achieve the best estimation you need to fiddle with these variables to determine which ones will fit the equation.

Instead of a clear answer of some numbers and sources I rambled about how difficult population estimates are. It's basically my long winded way of saying estimates will vary widely. Whitelaw(warning pdf) summarizes previous population estimates and determines the one's he likes best. He suggests an overall population for Neopalatial Knossos of between 14,000 and 18,000 individuals, which seems reasonable, however estimates as high as 80-100,000 individuals may also be probable. Unfortunately I do not have similar sources for Mycenae but Kelly et al. 2013 outlines their equations for population estimations that should give you an idea for how complicated variables can get and how difficult it can be to accurately determine population size.

TL/DR: population estimations can take centuries of archaeological survey and excavations as well as relevant historical and ethnographic research to determine accurate equations and analysis of variables. It's expensive and time consuming. Thus we often have several widely variable estimations for any society at any given time period based on concrete archaeological information.

Whitelaw, Todd 2004 Estimating the population of Neopalatial Knossos British School of Athens Studies 12:147-158

Warrick, Gary 2008 A Population History of the Huron-Petun AD 500-1660. Cambridge University Press [Selected Chapters 6 and 8].

Kelly, Robert 2013 A continuous climatic impact on Holocene human population in the Rocky Mountains. Proceedings of the National Academy of Sciences 110/2: 443-447.