I am developing a classic ABAP report in Eclipse using the SAP ABAP development tools Eclipse extension.
Is there a way to edit report text elements (text symbols, selection texts and list headings) in Eclipse directly or do I still need to open the program in SAP GUI to do that?
Yes, you can create text-symbols directly in ADT since SAP NetWeaver 7.31 SP14 or 7.40 SP08.
For creating a text-symbol you should utilize Quick-Assist Eclipse functionality:
text-XXX piece in any valid statement, e.g.
What concerns selection texts and list headings, no, they are still to be edited via GUI.
However, SAP implemented small menu entry for quick access to this function. Just hit context menu on any place of the source and select Open others->Text element.