It almost looks like they just put up brackets evenly spaced. Are they separate on actually on the molding?

If you don't like it, remove it. It will require some wall patching but not anymore additional painting than just painting over it.

I'm pretty sure individual blocks were nailed in place. In the different photos the style of the block even changes.

Also does this kind of molding require hand painting to do a good job or can it be airspray painted?

You should be able to spray paint as long as the detail is simple. The sides might be a little tricky - consult a painter in your area that can come to your house and give you the answer.

looks to me like they just nailed brackets and simulated the dentil with crown in one picture, chair rail in another and hard to tell on the smaller. You should be able to cut them loose and remove (assume they were nailed). You could always add a slightly larger ledger board where the old came off to cover the damage. Perhaps just replace them with some crown molding.