Translation:I do not like the subway.
Wa: Marks the topic. Replaces wo in negative sentences usually. Used in questions. Used with things that are already being talked about. Used with general instances of sonething while wo is a specific instance. Ga: Marks the subject (less important thing than the general topic). Used with things that have not been introduced to the conversation yet. Can imply contrast. Wo: marks object. Used with specific instances of something. "Niku wo tabemasu": I will eat this specific instance of meat. "Niku wa tabemasu ka". Do you eat meat? "Niku wa tabemasen" I don't eat meat "Niku ga daisuki desu" We weren't talking about anything remotely related to meat but I'm just putting it out there that I really like meat
I agree, but you could put it more simply. In a basic sentence in almost any language, theres an agent (or subject) doing something to a patient (or object). For example "he (the agent) likes her (the patient). は is used (in most cases) to mark the agent, while が is used (again, in most cases) to mark the patient.
You're almost right,じゃありません ( or ではありません) is technically the negative form of です, because they're both in polite form. じゃない and だ are the casual forms, but you can make じゃない polite again by adding です, so じゃないです.
You do this with other verbs as well. コーヒーを飲みません。 コーヒーを飲まないです。 I don't drink coffee. (飲みます is のみます, to drink).
You may notice the verbs conjugate a little differently in casual form. I'm sure they'll get into that at some point.
There shouldn't be a macron above the a in ja nai.
じゃない is used to negate nouns/pronouns and な-adjectives.
ない is mainly a verb-negating suffix; it's mainly used in the negative form of a non-past verb. It can also be a separate word, used as the negation of ある, to refer to something not existing or not being (there).
は marks the topic, not the subject, while the subject is often implied. If a new one needs to be introduced, が is used. To put it very simple, は is about equivalent to "regarding/as for x," so "as for the subway, I (implied, could also be he/they/you/etc.) don't like it."
I've also heard from other comments that は replaces を in negative comments, but this I'm not sure about the details of.