"I talk with my friend."
は is for the topic of the sentence, usually the person/thing that is performing the verb.
Due to context, 私は（わたし は）"I" is often implied/left out. So, は is not present in this sentence.
If you put 友だちは instead of 友だちと in this case, its saying "my friend talks" instead of "i talk with my friend"
I came here to comment on this vs. Another exercise as well. I am certain that the Japanese excersize did indeed say specifically "かのじょ と -は- はなしません" with that particle in there. Based on what folks are saying, I'm figuring that the difference is in regards to who the sentence is more about. So: 友だちとはなします Seems to be more about me and my importance to the context of the conversation, rather than my friend, where 彼女 と は はなしません Is less about me as a speaker, and the conversation focus is more about her. This is definitely just an educated guess though, if anybody knows better, please correct me!
Here are some literal translations
彼女とは話しません = "as for her, (I) do not speak with her".
彼女と話しません = "(I) do not speak with her".
友だちとは話します= "as for (my) friend, (I) speak with him".
友だちと話します= "(I) speak with (my) friend".
は only brings the topic up, the topic is whatever is preceded by the particle. Here is an article that explains topic and subject in Japanese really well
Yes indeed; they are similar and related. Both contain the part (called a "radical") of 言, meaning 'say/word'.
Other kanji with that part also have to do with words in some way, such as 読 (reading), 記 (writing), 訳 (meaning/translation), 詩 (poem), etc.
As for the right-side, which sets them apart, 舌 means 'tongue' and 吾 means 'I/me'.
To be slightly more grammatical: はな~ is the stem. はなす is the so-called 'dictionary form' (or rentaikei 連体形 in Japanese) and はなし is the 'conjugative form' (or renyoukei 連用形 ). The renyoukei is used to add all kinds of extensions, such as ~ます for polite speech (which itself is again a rentaikei!).
"To" does not mean "and", to is "subject + accompaniment" so for example: Tomodachi to hanashimasu = I talk with a friend. A becomes my because we know the context here is "I".
Table no ue wa ringo to orenji ga arimasu = Table's surface has an apple accompanied with an orange. In that sense, "to" is used to describe an accompaniment to the word before it.
The shimasu at the end is a verb-maker, it turns another word into a verb. In English we can usually translate it as "make" or "do". So in this case, I make talk. (We do this in the phrase "make small talk", for instance.) But talk is both a noun and a verb in English, so usually we would not use the same construction for that word.
Close, but not quite right. します (the neutral polite form of する, "to do") is indeed used to turn nouns into verbs, just like in English (e.g. "to do laundry" = せんたく する).
However, there is no independent します in this sentence, since the はな part is also not a noun in itself. It's the verb 話す（はなす, "to speak/talk"）in its neutral polite form: はなします.
You can use a similar construction to say "have a conversation", which uses the same kanji, but is pronounced hanashi and comes with a direct object particle: 話をします.
it's actually the same word, the pronunciation changes because of 連濁 "rendaku", you can just use 友 as a word as well but is very archaic, 友だち is the plural of 友 but for some reason they started using 友だち for singular as well, probably because it sounds nicer. You can find 友 as a word in some literature too from time to time and I would say that is more of a written word than spoken.