Selecting and copying multiple dynamics at the same time

It's not possible and not likely. Dynamics are attached to notes rather than points in time like chords. If you paste chords, they can be inserted onto any rhythm you have entered. If you paste multiple dynamics and the dynamic is supposed to be on the second beat of a half rest, what do you want MuseScore to do with it? It is impossible to enter a dynamic on the second beat of a half rest. Typically, dynamics are not put on rests, though I've occasionally seen this and it's possible in MuseSore. Should this dynamic move to the first beat? Should it move to the next note/rest or move only to the next or previous note? What if there's already a dynamic at that point? What you want or expect may change from one score to the next and may not be the same as my expectation.

What is possible: If you have the same rhythm (or even close) in two different places, you can copy from one place and paste into the other and use re-pitch to change the notes at the destination. If the rhythm is close, you may need to do a little adjustment of the rhythm in the default note entry mode. There are many tools, you need to use the correct tool at the right time.

Actually, unless I'm misunderstanding, this is possible, Just select the dynamics you want to copy (either via Ctrl+click, or select a range then right-click one dynamic and Select / All Similar Elements in Range Selection), then Ctrl+C to copy, then click the new start point, then Ctrl+V to paste. Works the same way as for chord symbols, keeping the same beat positions (as opposed to how it works for lyrics or articulation where it tracks the notes themselves). But it's true that you'd better have notes at those beat positions or it won't layout as expected.