Try a wash in warm, soapy water first as dust can get "stuck" on. I have washed Playmobil in the dishwasher on an eco setting without problems.
For polishing, I have used car polish or to remove stubborn stains the type of car polish used to remove liught scratches, but be careful with this - not too much, don't rub too hard.
Other members will have their own favourite methods and materials.