We have established trees, so I'm not really the best to advise!
We prune the new shoots (suckers) lower down the trees but leave the rest! I would say a young tree would benefit from thinning if looking crowded.
Feeding, I would say a little well rotted would do the trick! Our trees are in flower (nightmare if you have hayfever!) what is your tree up to?
Hope this helps!
PS Olive trees are tough, don't worry about pruning..............