Forgive me if this is overly simplistic since I'm not an engineer and I don't know your level of knowledge, but lift on an airplane is generated by air flowing over the wing. If you'd like to
see this effect in action take a piece of paper, hold it on each end and blow over the top of it and you'll see it start to float.
When a plane turns, it tilts or “banks” to one side. That tilt means the lift that normally pushes the plane up is now partly pushing it sideways. So the plane doesn’t get as much upward lift and can start to lose altitude.
To stay level during a turn, the pilot has to pull back on the controls or speed up to make more lift, neither of these options is available to a plane that has either lost engine power, or in this case has reduced engine power, just after takeoff. (and thus at low altitude)
As for taking off and landing you always want the wind blowing at you from the front to generate as much lift while using as little power as possible. That's why airports have so-called "active runways" so they can have planes taking off and landing into the wind.