Does a mole of the element uranium and a mole of CO2 have the same number of particles?

Yes. One mole of anything contains 6.02x10^23 "particles". In the case of the element uranium, it would be 6.02x10^23 atoms of uranium in 1 mole. In the case of CO2, it would be 6.02x10^23 molecules of CO2 in 1 mole.