My question is that is it possible to somehow mesh the geometry on picture with hex elements, 2,5D mesh? It s a cut out of a spiral bevel gear. When selecting 2,5D mesh the software won't allow me to mesh the body.
One more thing, can I convert the quadrilateral surface mesh into triangular mesh which basis is the former mesh?
That looks like it should be a good candidate for 2.5D meshing. Do you have mesh seeding defined on the solid? Depending on how that's defined, it could be getting in the way.
If you switch on the 2.5D colour icon:
then that will colour-code the solid according to whether Apex thinks it can hex mesh it or not. Green means yes, yellow means yes but with some action needed first (usually to resolve mesh conflicts), red means no (in which case you can try partitioning it to make it meshable). Have you watched the video on hex meshing in the Apex help? That's a good starting point for understanding the tools available.
1: you can get rid of these features just by deleting them. To get a meshable solid you only need to do this at one end of the solid, but the mesh will probably be better if you do it at both ends.
2: Most of the extra curves on this face will be OK, but the angled one here will cause problems for the mesher. You can get rid of this using the Vertex/Edge Drag tool; just drag the vertices at the ends of the curve to the nearest ones on the corners of the solid:
You need to get rid of this sliver face. There are various ways you can do this. I did it by creating extra vertices (using the Add/Remove Vertex tool) on the inner edge, then dragging these onto the equivalent vertices on the outer edge: