Will the new cells have the same genetic material as the parent cell or will each ceell have different genetic matireal?

Mitosis: It depends on what kind of cell it is. If it is a somatic (body cell) then it will have the same materials and everything as the parent cell.
 meiosis: But if it is a gamete cells then it requires the fusion of two different 'cells' and they combine *crossing over-the chromosomes from the different people combine together to get different combinations* and the new cells are haploid (half the amount of chromosomes) so the new cell will have both genetic material from both parents-paternal and maternal.