The 3rd sentence is incorrect. 話す（はな・す） is the verb in dictionary form, and it conjugates like 話します（はな・します）、話さない（はな・さない）, 話して（はな・して）and so on. You always need し or other hiragana for conjugation. Confusingly, there is a noun written as 話(without し), and reads as はなし. It means story, tale, talk, chat, conversation, etc. If you are using 話 as a noun, there should be no し. (e.g) 先生の話は長いです。 The teacher's speech is long. More confusingly, you can turn the 話(noun) into a verb by adding する。Usually we put を between 話 and する. 話をする（はなし・をする）　 As a verb, it means to tell a story, to talk, to give a speech etc.

1. 私は　英語を　話す。hanasu＝standard 2. 私は　英語を　話します。hanashimasu＝more polite/ formal 3. 私は　英語を　話ます。hanamasu＝should be 私は 英語を 話せます means I can speak you could also read 話 as hanashi For example, 彼の話(hanashi)は楽しいです。 その話(hanashi)が好きです。 話(hanashi)があります＝ I need to talk

The verb 話す　can be conjugated as 話します. So you can say: 英語を話します or 英語を話す (The use of pronouns is not imperative and it is preferably avoided) Usually they say that the short forms (話す，来る，行く) are infinitives, This is not really true, but this is the form in which verbs appear in the dictionary, and that is why they are also called "dictionary form". The difference between saying "話します" and "話す" (both meaning "I speak") is the level of respect you show to the other person. If you are talking to your father, boss, a costumer, you would say "日本語を話します" but if you are talking to a friend who is your same age or younger than you, you say "日本語を話す". Now 話し is not a verb, it is a noun, meaning "conversation". You can convert nouns into verbs by adding the verb "する". 勉強 means "research", but 勉強する is a verb and it means "to research". Of course "する" is the short form of します　so you can also say 勉強します (same difference of respect as mentioned before). So the noun 話し　can become a verb adding する or　します.

First 2 options are okay, but if you want to say that you can speak English, you should say 英語が話せます.

1. 私は　英語を　話す。 informal 2. 私は　英語を　話します。 formal #3 is not correctly written. 話 is read as "hana".