@pompelj
"I belive, that the skeleton now has 5 separate bones for the pelvis (coccyx, Pelvis_L, Pelvis_R, sacrum02 and sympubis01). Would it be good to group these bones in one bone "Pelvis"?"
Yes, exactly. You should attach them together to be 1 object using "Attach" in Edit Mesh or Edit poly rollout.
"Also, each toe and finger is now 1 object which should be I think separated each into 3 separate bones (except big toe into 2). Is this ok?"
Yes, exactly.
"If I manage to do one side of whole skeleton correctly (detach the bones, place Pivot Points, separate toe and finger bones), could then I just do [select the side that is done] - [Tools] - [Mirror] - (Transform, Mirror Axis: x, Offset - place correctly, Clone Selection: Copy, Mirror IK Limits and press OK)?"
Yes, but you have to make sure that the currently active pivot is in the center of the body when you mirror the bones or the mirrored bones will not be in the correct place. I suggest you use the working pivot by first editing it to be in the center of the pelvis and then click the check mark and then "Use Working Pivot" as shown below.
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After the mirror operation is complete, switch coordinate system back to Local for subsequent rotation of bones to create poses. Also keep in mind that you don't want to mirror all of the bones, for example the pelvis, the ribcage, the spine , neck and head don't need to be mirrored.