Yes you can put stainless steel milk pitchers in the dishwasher. For the painted stainless steel milk pitchers it is not adviced to put them in the dishwasher. Those need to be cleaned manually.
The diameter is also a important feature for the levelling tools, seen as with regular tampers, you have different sizes. The most common size is 58mm, this is used on brands such as Faema, Rocket, ECM, Marzocco, Bezzera, Nuova Simonelli and Victoria Arduino. A other size is 57mm, this is mainly used on Cimbali espresso machines. In a lot of cases the 57 and 58 mm tampers can be exchanged. A completely different size is the 53mm coffee leveller, this is used on espresso machine brands such as La Spaziale and San Marco.
Coffee levelling tools are made by various brands such as Motta, Rocket, Pullman, JoeFrex, ECM, Bravo and Asso.