Can two mosfets (p&n, some characteristics) be used as current sources simultaneously? And what happens if the Vgs voltage change?
Yes, this can be done.  It can even be useful in some cases, although not usually with the load where you show it.

Let's consider your circuit without Rload, just the two transistors connected together directly.  We'll consider this node the output.

If the two current sources were ideal and exactly matched, then the output voltage could be anywhere between the supply rails.  If one of the sources was set to even a little higher current than the other, that source would have low voltage across it and the other with maximum voltage across it.

If you arranged the input signal to vary the two current sources oppositely, then you would ideally have a infinite gain amplifier.  When the input is at one side of the threshold, the output slams one way.  When at the other side, the output slams the other way.

Real current sources, such as implemented by these transistors, do not have ideal infinite impedance, or course.  Put another way, their current is at least some small function of the output voltage.  In that case, if the two were exactly matched, the output voltage would be in the middle.  The mismatch in the current setting of the two sources would create a output voltage offset from the middle.  This output mismatch voltage would be the mismatch current times the parallel impedance of the two sources.

The result can still be a very high voltage gain.  If designed for this application and operated in the right region, the MOSFETs will look like current sources with reasonably high impedance.  Small changes in gate voltage can have significant effect on the current.  Together, these two effects cause a large gain.

A large negative voltage gain isn't the only purpose of such a circuit, but it is one example of how such a configuration can be useful.

For discrete designs, BJTs are usually better for this.  The current thru the collector is rather independent of collector voltage over a wide operating range.  However, if this is in a IC, then a mix of BJT and MOSFET is usually not available.  The characteristics of individual transistors can also be better controlled and better matched between two devices, so the circuit you show can be useful.