Can I insert a Tab in a cell, like using the tab key in Word ?

I don't think so. Why do you want to? What exactly are you trying to accomplish?

I have 2 columns of dates with headers in row A, with a single cell for the header for both cols.

I tried to centre the text over both cols with spaces in front which didn't work well, R/L justifying the text didn't work and I don't like merging cells as it affects Sort. Is there another way

I don't understand what you mean. Would you please attach your sheet?

Avoiding merged cells is a good idea.
How about the "center across selection" formatting ?

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