Yes you can. You are under no obligation to leave anything to a child. But said child might take a S117 objection if they feel you failed in your duty to look after them.
You are incorrect to say 'their' inheritence. It is your money to do with what you wish. The exception to this is a spouse.
Not sure if its possible but if property is part of the estate could you leave to the grandchild with a lifetime use clause for your own child / children.
Yes you can but the tax free threshold to a grandchild is substantially lower than form a parent to child. Your grandchild would be charged 33% CAT on any amount over €32,500