A Russian friend helped me with this. I thought since people say that щ is shch that I was supposed to pronounce first the sh sound and then the ch sound. But that isn't right, and I think that transliteration for the letter is misleading.
When I say sh in English (I'm American) I pronounce it with one side of my tongue on the roof of my mouth. Turns out that is the way to pronounce the щ sound. The ш is made with just the tip of my tongue curled up and almost touching the roof of my mouth. I had never made a sh sound like that before in English. But my Russian friend said it really helped my pronunciation to make the distinction.
Simple explanation: Articles don't exist in Russian and since the word "This" was placed in Russian, they'd say "this woman". This is no different from English in that if I said "This woman is in the park", I don't mean another woman or some general woman. I mean THIS one. Эта 'this for feminine nouns' can never mean "The".
Confusion about the words this and that:
Это 'this/that/it' is not the same as Это 'neuter form of Этот' meaning "this". Этот, Это, Эта, Эти. "That" would be translated as Тот, То, Та, Те.
"Это такси" could therefore have two meanings. "This is a taxi" or "This taxi".
i've noticed there are a lot of cognates between russian and english! i think this is in part due to russian aristocracy in the 18th/19th centuries speaking french to each other. french and english have a lot of cognates, so there must have been some loanwords passed between french and russian. even merchant classes spoke french, i believe, and the extent to which french was used in the noble classes was so much that sometimes they were more fluent in french in certain specialised topics than they were in russian.
We have a winner! As a somewhat interesting (I hope) aside, Tolstoy's War and Peace has a lot of French dialogue for that reason -- you have to be fluent in both Russian and French to read the original (unless you use the footnotes, where the French has been translated into Russian, of course).
As far as I understand, most nouns that are masculine or neuter and end in a consonant, you use the "-e" ending for prepositional case (as in в магазине). When you use где to ask a question, things are a little different, but I bet they'll get to that later in the lessons.
schizorb shows how to handle feminine nouns below.
Actually "библиотека" and "квартира" are femenine. Mastersword83 is right, most nouns have the "-e" ending in prepositionsl case:
Квартира - о кваритире (f)
Стол - о столе (m)
Окно - об окне (n)
If the noun ends in "ь", the endings for prepositional are diferent:
Соль - о соли (f)
Конь - о коне (m)
If the noun ends in "ия", "ий" or "ие", we use "ии" in prepositional case:
Армия - об армии (f)
Санаторий- о санатории (m)
Ударение - об ударении (n)
Эта женщина БЫЛА в парке. You can use the verb есть in past or future tense - in past tense it's typically only to say someone was somewhere - if you want to say they were performing an action then you would use the imperfective form of the verb. For future tense, you can simply say Она будет в парке if you want to just say she is going to be in the park.