Hello, Lindsay.

It is very please for me that you are interested in Russian language.

I would like to help you with it:) I have only intermediate in English but I hope it will be enough for this task:)

1) Yes, you are right. The first one is right. If you want to say "I can speak a little Russian", it would be:

Я умею(or)могу немного говорить по-русскИ. ("can" = "могу" = "умею" in general)

или 

Я немного говорю по-русскИ. (it sounds more literary and smoothly:)

2) The second of your sentences ("Я бы немного говорить по-русский") includes mistakes and you shouldn't write and speak like this. But maybe you read like some of this variants?:

Я бы немного говорить по-русский

Я бы ХОТЕЛ УМЕТЬ немного говорить по-русски. - it means "I would like to be able to speak a little Russian"

Я бы ХОТЕЛ НАУЧИТЬСЯ немного говорить по-русски. - it means "I would like to learn a little talk Russian."

или

Я бы ХОТЕЛ немного ПОГОВОРИТЬ по-русски. - it means "I would like to talk a little Russian" (I would like TO HAVE A TALK or HAVE A CONVERSATION with someone)

3) About difference in the meanings between your two sentences:

Я могу немного говорить по-русский
или
Я бы немного говорить по-русский

As you see, if in Russian we use "БЫ" - in English we use "could", "should", "would" and never "can", "will". 

"Would you like a cap of coffe?" - "Хотели БЫ вы чашку кофе?" ("or something else")

"Do you want a cap of coffe?" - "Хотите чашку кофе?" ("we have only coffee and you don't have any choiсe". It is very directly and tough.)

"I could help you." - "Я мог БЫ помочь тебе" ("if you want" or "if I have a time" or "If anyone else can help you")

"I can help you." - "Я могу помочь тебе" ("I am shure that I can help you anyway! You can rely on me.")

4) About difference in the meanings between "говорить" и "поговорить":

"I can speak a little Russian but I have not someone who could talk with me." -

"Я умею ГОВОРИТЬ немного по-русски, но нет никого, кто мог бы ПОГОВОРИТЬ со мной"

So:

"ГОВОРИТЬ" like "SPEAK". "ГОВОРИТЬ" - displays the fact of speech rather than its content. It is also used when we specify the language in which we speak or when a person makes a public appearance. You can "говорить" even if you are alone - "Bla-bla-bla-bla":)))

For example:

"Я ГОВОРЮ вслух и даже пою в ванной, когда остаюсь один в квартире." - "I say out loud, and even I sing in the bathroom when I left alone in my flat."

"Моя жена сказала, что я ГОВОРЮ по-русски, когда я сплю". - "My wife said that I speak in Russian when I sleep."

"Моя цель - ГОВОРИТЬ на нескольких иностранных языках" - "My goal is to speak several foreign languages" (to can)

"ПОГОВОРИТЬ" like "HAVE A TALK, HAVE A CONVERSATION". You cann't "поговорить" if you are alone:) You necessarily need to interlocutor.

For example:

"Я хочу ПОГОВОРИТЬ с дочерью об её школе." - "I want to talk to my daughter about her new school."

"Когда мне одиноко, я звоню друзьям, чтобы ПОГОВОРИТЬ." - "When I'm lonely, I'm calling friends to talk."

"Я могу ГОВОРИТЬ собаке: "Сидеть" и "Молодец". Но я не могу ПОГОВОРИТЬ с собакой, потому что собаки не умеют ГОВОРИТЬ." - "I can say to my dog: "Sit" and "Good".
But I can not talk to my dog, because dogs can not speak."

I'm not sure of my linguistic and pedagogical talents but I hope you will be able to understand me in general:)

But if I explained well, then write your own colorful example of the difference between "ГОВОРИТЬ" to "ПОГОВОРИТЬ" (in English or Russian).

Good luck!