The main advantage of variable sweep wings is that they reduce drag over a wide range of Mach numbers.
However, the variable sweep wings are not being used in present day aircraft for a variety of reasons.
- The variable sweep wings are heavy and mechanically complex, affecting performance and maintenance.
- The swing mechanism takes up too much space inside the wing that could be used for fuel.
- It is difficult to position hard-points in the swinging part of the wing, affecting payload.
- Advances in aerodynamics and better engines mean that the drag reduction using varying the wing sweep is not so critical anymore.
- Also, the newer combat aircraft are not trying to outdo each other in speed, trying to gain the edge using better situational awareness, stealth etc.
However, the most important reason for variable sweep wings falling out of favor is that they are nearly impossible to be made stealthy. One way to make the aircraft stealthy is to reflect the Radar energy away from the source. In order to achieve this, the wings of stealth aircraft are designed in a specific way.
However, if the aircraft have a variable sweep wing, this condition is all but impossible to achieve. If stealth is still required, it has to be through more Radar absorbent materials, which further increases weight and maintenance requirements. The last variable sweep aircraft, B-1B, for example is designed to be a low level penetrator, unlike B2.
Because of these reasons, the variable sweep wings have fallen out of favor.
As for the second question, the wings of F22/F35 has basically a trapezoidal wing configuration, which gives a high performance at high speeds.
However, the main reason for using this type of wings is the excellent stealth characteristics they provide compared with other type of wings. One disadvantage of this type of wings is that their low speed performance is not up to the mark, but this has mostly been overcome by the use of improved control surfaces (like flaps, slats etc).
Interestingly, USN considered a variable sweep F22 for carrier operations, but the project was ultimately dropped.