Numbering Introduction and Conclusion? In research papers, should Introduction and Conclusion sections be numbered or non-numbered? What does the scientific paper etiquette suggest? Furthermore, in either case, should they appear in the Table of Contents?

If the answer depends on the research field, please elaborate. I'm in electrical engineering, but do occasionally write mathematical papers as well, so those two fields are personally of highest interest.

On a side note, in case someone confuses it with the Introduction section, I am quite sure that the Abstract section should be non-numbered either way.
It's not field-dependent, it's a journal-dependent issue. Some use a format where everything is numbered, some use a format where nothing is numbered, and still others leave it up to the authors to decide.

However, when sections are numbered, everything in the main text should be numbered, including the introduction and conclusions. You don't skip numbering those sections but add numbers for the rest. That doesn't make any sense. (End matter such as acknowledgments and supporting information may be handled separately.)

The best advice is check the style guide for your journal.