"Many people live in Mexico."
Translation:Multaj homoj loĝas en Meksiko.
Some people say that, but the Esperanto Academy recommends that the country should be called Meksiko. The capital city is Meksik-urbo.
I don't think that's exclusively true. If you are pouring water in a bowl (like in the bowl and pouring water) you would use "en" but not the accusative, but if you were filling the bowl with water, you could use "en" but would need to use the accusative to show the water is going into the bowl.
I gather that prepositions negate the accusative always, because they are doing its job for it. I.e prepositions mark a word as receiving an action. We see 'in' after a verb, we know something is being put 'in' the bowl, the bowl is the object.
You're making things unnecessarily complicated. Quite simply, the accusative is not normally used after prepositions (except in specific situations, which will come later in the course). That's all you need to know.
Because there isn't an action being done TO mexico. We are just talking ABOUT it.
If you mean because Mexico isn't the direct object of the verb, that is correct. More precisely, "Meksiko" follows a preposition. After prepositions you don't normally need the accusative ending -n (except in special situations involving movement, which will come later in the course!)
There are some examples in PIV (the most important Esperanto dictionary). "La tro multa parolado lacigas lin" (Too much talking tires him), "De tro multa scio krevas la kranio" (From too much knowledge the skull bursts), "Li montris multan paciencon" (He showed a lot of patience). You could also use it with collective nouns, e.g. "Mi havas multan panon / multan monon", although I would be more likely to say "multe da pano / multe da mono".)
Yes, in a sentence like this there's not really any difference between "persono" and "homo".
In Esperanto, adjectives are adjectives, and nouns are nouns. You don't use adjectives as though they were nouns. You could say "Multaj loĝas en Meksiko", and that, as in English, means "Many live in Mexico", in other words it's not complete in itself, and you use it when you've already introduced the noun earlier. For instance, in English you could say "Some Canadians live in the US, and many live in Mexico". In Esperanto that would be "Kelkaj kanadanoj loĝas en Usono, kaj multaj loĝas en Meksiko".
When you add ge- it means male and female together, i.e. men and women, boys and girls etc. But "homo" already means either male or female, so it's pointless to add ge-. The same for the word "infano": "infanoj" already refers to children of both sexes, so there's no need to add ge- in front.
No, "homo" just means a person which includes female persons, so it's not correct to add -in-. If you specifically want to say "man" or "woman" use "viro" and "virino".
"Popolo" means "people" in the sense of an ethnic group, a tribe, or something like that. You can also use it for "the people" contrasted with the ruling class, e.g. "La popolo ribelas": The people are rebelling. But you don't used it for the simple idea of a number of individuals. That would be "homoj" or "personoj".