Yes, OpenMandriva use rpm packages (rpm4) and DNF.
I use from time to time Opera browser myself and I can say that it works without problems on OpenMandriva Lx4.
So yes, opera working fine. Same with Google Chrome.
I did not test Skype but we have it in the repository. You can download by following the command:
thx look it works nice. But did you know how to install everthing to c++ development? Some say mate is available for openmandriva? Did you know how to install it? find it out, sudo dnf install mate-desktop
So XFCE will not be available on openmandriva?
MATE is in unsupported repository so you have to enable it before to install. Then you may use dnf install task-mate if you want MATE desktop as is or dnf install openmandriva-mate-config (suggested) you you want to use a preconfigured MATE desktop in OpenMandriva style. Of course in any case you may change the configuration of you desktop at any time.
The only part it is known not working in MATe is engrampa (archive manager) so actually i suggest you to use xarchiver or file-roller instead.
If you experience some issue with MATE please open a new thread.