so if you use a genitive preposition, the other words that can be in genitive form must also comply? Is this true only for genitive prepositions, or when there are any genitive words included? Would there be a case where этого would be the only genitive word in the sentence? I would think not, since you can't apply the 'of' rule here, but would like clarification/confirmation. Thank you.
возле is a genitive preposition, words after it must be in the genitive case. You can think of it as meaning "in the vicinity of", as "of" is a genitive word in English.
You may have been under the impression that any word after a preposition gets the prepositional case. This is not true. The prepositional case is badly named because it is only used for a small number of prepositions, mostly those referring to a fixed location.
Just in case this helps: http://www.russianlessons.net/grammar/pronouns.php
As stated, этого is a genitive case of это. You can find prepositions that require genitive case here: http://www.departments.bucknell.edu/russian/language/prepgen.html
Возле is one of them. Hence возле этого.
Russian doesn't have a word for "the". Although sentences using этот can sometimes be translated using "the," you never need to. Offering that as a possible translation, while technically accurate, probably is contributing to confusion.
этот always means "that" or "this," in the sense of "the one we're talking about."
It's probably worth reporting this. It seems like this one of the inconsistencies you sometimes see with Duolingo where the scrolling offers you several translations and then marks you wrong for using one of them! I suppose it's partly because Russian is still in Beta phase. This shouldn't stop us from realising what a brilliant course this is however!
Russian doesn't differentiate between definitiveness and indefinitiveness in nouns. это mean this, but it can also be translated as the (and if I remember correctly also that) depending on the situation. In this Duo course they've made the decision of mostly translating it to this. On the reverse tree, I think; it's mostly translated as the.
This confusion is due to the fact that languages work differently. Whenever a category is missing in a language like this, it's impossible to say a word has the same meaning as in another language where the category excists. It's good to compare, it's even better to learn to look at the world through the new language.
First of all, it's этот, not етот. As for the various declension forms, specifically for этот, a Google search for "demonstrative pronouns Russian" (without the quotes) will yield endless tables and relevant information. In general, for declensions and conjugations of other words (not necessarily demonstrative pronouns), I like using openrussian.org.
It is not how you would say it. "Anna is near the taxi" is what would be said. Or if there were lots of taxis and you had to point then "that taxi". This and that are acts of specifying. "This" if you are close or you are holding the item, that if you are away from the item. To use "that taxi" when there was only one, would be an exclamation of some sort (either good or bad).
Your comment seems incorrect to me. 1. You would say "Anna is near the taxi" only if a specific taxi was previously discussed. If you haven't talked about some taxi prior to this sentence, referring to "the taxi" would raise questions. 2. Say there's only one taxi, and it's a 100m away, pointing at it and saying "this taxi" is bad English. Proper English is to address it as "that taxi", and there would be no exclamation whatsoever in this context. By the way, in the meantime I've actually realized that the two concepts in fact exist in Russian, they are этот and тот.
Here is a good resource on genitive case that will get you started. The entire website is a great companion for Duo — I especially appreciate it as a resource on perfective and imperfective verbs, when you get to that point.