The static port is designed to not be affected by the relative wind. It’s typically a small pinhole perpendicular to the relative wind, and at those sizes the viscosity of air is such that it won’t flow into the port. Static ports are also often duplicated on both sides of the aircraft, so that ram air forced into the port by a sideslip does not effect readings.
As for carb heat, there are several reasons why you don’t use it continually. One is that hotter air can cause detonation. Another is that you lose power when you apply carb heat, because you’re feeding hotter, and therefore less dense air into the engine. A third is because carb heat typically pulls unfiltered air, which is to be avoided as much as possible. And finally, leaving carb heat on all the time defeats its purpose. You may enter a condition in which the carb heat moves the venturi temp into the icing region, and ice will form. Then you’ll have no way to get rid of it.
Carb heat is not a guarantee against ice formation. It’s a way to change the temperature of the air going into the carb so that you can change the status quo. If ice is forming, adding heat may get rid of it. If ice isn’t forming, it may be because it’s too cold, and adding heat will put you into the ice formation region.
Incidentally, your instructor has probably told you this already, but if you apply carb heat at cruise because the engine starts running rough and you suspect icing, do NOT just pull it on and then switch it off right away. Intermittent application of carb heat may just melt ice and cause it to reform once you shut it off. Once you turn on carb heat, leave it on until the engine is running smoothy, and then wait a little longer. This is also why you pull carb heat on in the pattern - not because you’re more likely to get ice at low power, but because IF you do, the application of carb heat itself can cause the engine to quit completely if it dislodges a chunk of ice into the carb. So once you put on carb heat, you leave it on while you’re near the ground. Just remember to put it back in again on the go-around, or you won’t develop full power.
I imagine you’ve been told this already, but carb ice forms because of the temperature drop in the venturi of the carb - a drop that can be as high as 30 degrees C. So you can get carb ice at almost any ambient temperature.
Couple of other notes about the use of carb heat: If you don’t have a CAT (carb air temp) gauge, never use partial heat. You can induce icing that way, and then you’ll have no way to fix it. Without that gauge, you’re either full-on, or off.
Also, when you do the run-up, one of your checklist items will be to pull the carb heat control and look for a drop in RPM or manifold pressure. I know a lot of pilots who just note the drop, and push the control back in. Be more careful than that. The carb heat test has two purposes - one is to verify that the control is working properly. The other is to clear any ice that may have been formed during the taxi. Just pulling heat on and then pushing it off won’t tell you if there was ice, and can make it worse. So when you apply carb heat, watch for a drop in RPM, then a rise. If you see a rise, it means there was ice. Leave the heat on until the RPM stabilizes, then wait another 10-20 seconds to make sure everything’s okay.
Also, another little safety tip to get into the habit of - when you pull the carb heat during the run-up, keep your hand on the control until everything’s good, then push the control in. If you take your hand off the control, it’s just that much easier to forget to shut off carb heat before takeoff.
Hope this helps.