Palming can't be defaulted on, so yes, if you want to hide something better than just a Concealment test, you need to know how.
And yes, if a bunch of people start studying you, the normal gun in a holster under the coat may be spotted by some. If on the other hand you're a bit away and they're merely giving you a glance, or just looking at your face, they get an extra -5 (-2 distance, -3 not paying attention to the right details), making it near-impossible to spot. If you're a guard quickly checking the crowd for faces that are up to no good, you won't notice the concealed gun. If you're a bodyguard facing the one menacing guy walking towards you, it's a lot easier to spot a hidden weapon, unless they took effort to hide it.
So if you're walking the streets, only cops may notice you're carrying, and only if something else draws their attention. The rest won't know.