Overtaking cyclist on Country road

Do we need to indicate Left while overtaking cyclist on country road??

Is this correct : check traffic back/ ahead first, then move towards center line (with no Left indication), reduce speed while passing the cyclist and then join back the lane with increased speed. ??

I would say:

If you cross the centre line - indicate

If you don’t cross the centre line - don’t indicate

The car will be in the middle of the lane divider ( 2 lanes, one in each direction ).. in that case, should be still indicate??

Yes, if you cross the centre line in any way, I would indicate. There is no clear or fixed rule for this. The closest thing is that you should indicate when moving sideways in a significant way. And crossing the centre line is significant I would say.