Hello, hello, I've got a question that I feel I should know the answer to by now but I'll ask anyway. When I was in Germany I noticed many people sound like they're saying "ich hab" instead of "ich habe" and mostly teenagers did it. Is this just their faster way of saying it while "habe" is just technically the correct way?
Yes, exactly. It's about speeding things up or making them easier.
Ich hab is simply faster and it's also really not a thing only younger people do. It's probably as common as saying "it's" for "it is" in English. So we don't perceive it as wrong or strange either. It's just natural spoken language.
We do this with most verbs when using the first person singular.
Examples: "ich komme" > "ich komm", "ich fahre" > "ich fahr", "ich sehe" > "ich seh"...