Is this suppose to be a comedy

It's not supposed to be a comedy at all, it's an example of noir. The characters are intentionally over the top and even the hero has his faults. As for the dialogue, the screenplay was very faithful to the book, almost verbatim,, minus the curse words.

'Cracking foxy' was directed at the cops by Bogart, something along the lines of "Sorry I got off on my hind legs, boys, but the news of Mile's killing upset me, and you birds come here cracking foxy".

Before I give you my opinion,from the context, what do YOU deduce it to mean?

No, it's not a comedy; but, yes, there is a relatively large amount of humor in it (definitely more than in most crime movies of the time).

Also:
Yes, Joel Cairo is most definitely gay. The audience is told that about as explicitly as was possible at the time (due to the Production Code rules) before he is even seen on screen. When Spade & Effie comment on Cairo's business card being floral scented and then give each other that little raised-eyebrow look, that's the big bright neon sign telling the audience that the character being introduced is gay. It may seem a ridiculous bit of stereotyping now, but at the time that was the tool that they had to signal that to the audience.

As for how Astor & Bogart play their roles: It's worth pointing out that both the Brigid and Sam *characters* often are play-acting themselves for various reasons. For example, that's the whole point how we see Sam reacting in the hallway after blowing up at Guttman: as soon as the door closes he is immediately calm, looks at his own hand shaking from "playing" enraged, and chuckles a bit to himself; he never was really angry to begin with, just playing it that way for effect. That's why there a couple times when Sam's smile is more fake-looking than anything else I've ever seen Bogart do: Sam isn't as good of an actor as Bogart is, and Bogart is playing Sam's playacting not being as seamless. And Brigid's acting (she is almost *always* conning somebody or other) isn't quite as good as Sam's, which is why Sam can see through most of her acting / lies throughout the movie (and tells her, and us by extension, as much). In short, Bogart and Astor aren't acting poorly; Sam and Brigid are acting poorly and Bogart and Astor do a good job of portraying that fact.

"Some of those of those lines....' I'm a liar, I've always been a liar'. 'You ll be slapped and like it' 'I like to talk with a man who likes to talk to a man ....' 'He was cracking foxy'."

It's "tough guy" talk of the time.

It was infused with the culture of the 40s. Years from now, people will look at movies from today and say similar things.

It has moments of humor, but it's not a comedy.