How would you say "my father is smoking" as in "my father is smoking because he's on fire"?
You had my curiosity, but now you have my attention. Lignot for you
Again, I think the english should be "My father is smoking tabacco" or the Japanese should be 父はすっています. One sentence has direct information, the other calls for an inference. Its not a direct translation.
As I mentioned in another comment, it's a set phrase in Japanese. "To suck tabacco" just means "to smoke" in Japanese.
There is also 喫煙する but I don't think it's used much.
You only said he was smoking, not what he was smoking
Isn't it correct to say 父は吸っています ? Is タナコ needed?
Why isn't this お父さん?
Because you use the humble form when talking about your own dad. ちち