Nose Diving Plane

That depends if you're using physics or manipulating your plane's transform directly, modelling the physics of a real plane would give you this effect if you give the plane an up force relative to its forward velocity so it'll naturally drop under gravity if it's not moving fast enough. Use angular drag to make the plane level out after rotating with add relative torque.

If you're not using physics you'll have to create a target rotation and turn it into a quaternion or you can use a look at function. You can find speed with rigidbody.velocity.magnitude (this will be absolute speed and not forward speed which is relevant for aircraft)