Absent any wind, a single engine prop aircraft will usually turn opposite the direction the prop turns when you are at high power settings. In most western aircraft, this manifests in a left-turning tendency and you need to use right rudder to correct it.
Once you get wind involved, the airplane will “want” to weathervane into the wind. You only have so much rudder authority to counter that, so certain wind conditions are fairly unflyable for these types of planes. There are also methods for using ailerons on the ground when dealing with winds - this will help prevent the plane (especially high wings) from tipping.
For landing, there’s less of a concern for the turning tendencies from the engine, however, you want to always try to land with the aircraft’s longitudinal axis and (big and) flight path aligned with the runway. Though touching down in an offset heading (“crab”) is often the appropriate technique for airliners and fighters, it is not appropriate for most light GA aircraft. A crab or any lateral movement can sideload and damage the gear and/or jerk the nose of the plane and cause loss of directional control.
And yeah, the sim handles crosswinds weirdly. Suffice it to say, as with earlier, too much crosswind is going to make it fairly uncontrollable, but there are some “sim-isms” that compound. Make sure you check the weather. Career mode uses the historic weather that existed at your designated departure time (within the last 24 hours). It’s not always clear what that will be unless you are used to their wonky system. Even then, it can overdo it. Here’s some advice on how to deal with the career mode weather system. Anything more than a 12-15 knot crosswind component in a 172 is going to be rough, even if you have a good setup and experience.
Also ensure you don’t have some sort of control binding that’s pushing the rudder over inappropriately.