だいじょうぶ means OK, alright, no problem... etc. そうだね/そうですね means you are agreeing with what the person just said. It's like "yeah hey?"

Maybe a useful way to look at it could be to think of が as meaning"the". So, as Rumina previously mentioned, わたしが would emphasize the fact that it was you. "I am the one who ate the apple". Versus regular old は, just stating that "I ate an apple". Good luck! This question will keep on coming up for ever and there is no simple, universal answer!

しょう is more like "let's". しょうか is more like "shall". As you can see, the only difference is the question particle か. おどりましょう = Let's dance. おどりましょうか = Shall we dance?

Don't worry about all the meanings unless they are relevant. Whatever the reason was you stumbled upon the word in the first place, learn that meaning by understanding how to use it in a sentence. That's my take on that

Hmm... it's weird, even in English, if you go around introducing yourself with "my name is (name)". Probably best to just say "Hi, I'm (name)" "Hajimemashite, (name)desu" is the most common introduction. After both people are done introducing themselves, you should both then proceed to say "Yoroshiku onegaishimasu", which more or less translates to "nice to meet you". In a more formal situation, such as work, "(name)to moushimasu" is best to use. Once again, after both parties are done introducing themselves, you should both say "yoroshiku onegaishimasu". Or, if you want to be extra polite, "yoroshiku onegaitashimasu". *Note - If you are introducing yourself in a work-related situation, you should include your company name before your own name and the "no" particle to indicate you are that company's employee. For example: "Hajimemashite, Microsoft no Joshua to moushimasu" Also, notice how I did not once use "watashi" in any of these introductions. To answer your second question, pronouns in Japanese are not used very frequently.

ともだちとはなしているときはけいたいでんわをつかうことはしつれいですか。 Maybe...

Very similar to the Canadian "eh". It's hot eh? あついですね