1) In principle all radiation can be "shielded". Radiation could be in the form of particles or electromagnetic-waves: in certain cases rather than shielded it is better to talk about attenuation of radiation cause just a part of the intensity of the incoming radiation will be "shielded" i.e. the intensity decreases but a part of the radiation still goes through the material
2)The thicker the material the higher its attenuation properties. Regarding the density we have to specify what type of radiations we are talking about: for instance in the case of neutrons the most effective materials have low density while for gamma radiation the opposite is true.
3)Again it depends on the radiation you ant to attenuate: for neutrons you can use Boron doped Polyethylene, for gamma and x-rays you can use Lead (or Tungsten its even better but more expensive), for alpha particles a thin foil is often enough...
5) if you want to evaluate it yourself you put a radiation source on one side of the shield that you want to test and on the other side you place a radiation detector or counter... there are also some tools online that allows to simulate this type of experiments have a look for instance at www.nucleonica.com