What does it mean to be on a first-name basis?

Can I say "elementary" or "fundamental" instead of "basic"?

Yes, that's correct! They are synonyms for each other. Ex: I want to learn the fundamentals of coding. Ex: I only know some guitar basics, but I can teach you.

Who does "as" refer to?

"As" in this case is a continuation of the previous sentence and is not beginning a new sentence, there is just a pause in between. So the full sentence here is "they are best known for their traditional role as fire dogs." "As" here is referring to the Dalmations being fire dogs.

What does "been a while" mean?

"Been a while" is short for "it's been a while," which is an informal expression meaning that it's been a long time since someone has seen someone/something. Iron Man has said this as a greeting to Dr. Banner, as it's been a while (long time) since they last saw each other. Ex: A: Hi Kathy! It's been a while, how are you? B: I'm doing great, how about you? Ex: It's been a while since I went biking. Ex: My driving skills are a little rusty, as it's been a while since the last time I drove.

Is the expression "be clear" used often? What does it mean in here?

Yes, the word "clear" as used in this context is used quite often. In this context, to be "clear" about something means to be very direct or specific about something or to give very detailed instruction or explanation. Ex: They were clear that if we trespass, they will call the cops. Ex: She made it pretty clear that she doesn't like me.

What does "ploy" mean? In what circumstances could I use it?

A "ploy" is a plan or action intended to give a person, group or organization an advantage in a given situation. It has a slight implication of dishonesty. It can be best used when describing the activity of someone or something other than the speaker. Ex: He's been acting nicer to the boss lately. It's all a ploy to earn a promotion. Ex: Social media companies promising better privacy is just a ploy to improve their reputation.