"I do not talk to him."
～ません is present/future tense negation. "Do not". "Did not" would be ～ませんでした The particle と means "and", like when you list things.
In general, Japanese omits mentioning the speaker. So literally the sentence says "And he do not talk", but when you add the implied "I" (私と) it becomes "He and I do not talk", which can be interpreted ti mean "I do not talk to him".
Good question. As an English speaker, you can think of "composite particles" (as I like to call them) like「とは」and「には」(to name a few) as serving the role of the first symbol (in this case,「と」, "with") while also setting the topic of the sentence to the target of the particle. So in this example, the difference between 「かれとははなしません」（彼とは話しません）and「彼と話しません」is the difference between simply saying "I do not talk with him" and adding the emphasis to "him". So: "I don't talk with him". Does that make sense?
Yes, because "ni" indicates "to", "at", "where" is happening the actions and "ha" indicates what's the "subject" or about what we're talking about. If the subject it's also "to", "at", "where" the action is happening, then they will be used together. "Kanojo ni ha hanashimasen". To her, I do not speak. If it was "Kanojo ha hanashimasen" then I think it would mean "She does not speak".
Yes. The kanji 話 (はなし) alone means a conversation, story, etc., but it can also be used as a verb stem for 話す (はなす) - to speak (う verb). You should also take a look at this Wikipedia article for more info on Japanese verb conjugation in case you're interested: https://en.wikipedia.org/wiki/Japanese_verb_conjugation/
Ohh! ありがとう. Thanks very much. That is clarifying. I gave a look at some verb conjugations before, but was still confused about that one. The link didn't work though. :( I just started focusing on Kanji now that my duo's course is finished, hope I can find some way to continue learning. Duo should give us more units :) Thanks again Mrr.
Sorry, the link wasn't working because I added an extra / character. This is the correct link: https://en.wikipedia.org/wiki/Japanese_verb_conjugation You could also try this app if you want to learn some more, but it teaches you words from random JLPT (Japanese Language Proficiency Test) levels, not ordered from the easiest to the hardest, it also teaches sentence structures, verb conjugations, etc.: https://www.lingodeer.com/ And you should also take a look at the N5 (easiest) vocab list: http://www.tanos.co.uk/jlpt/jlpt5/vocab/VocabList.N5.doc to see how many words you already know. (Note: Some words should be written using kanji, but aren't in the vocab list) If you're unsure about how a kanji is written (stroke order), how it's read, or its meanings, or just need a Japanese dictionary, try this website: https://jisho.org/ I think that's about everything :P