I need to select multiple cards (let's say after a filter operation) to add them in a checklist of another card. I do not see any way to perform this operation. Another close use case I have is to perform multiple cards edits: like assigning the same member to multiple cards or adding the same label to multiple cards.
Some of the tasks you mentioned can be performed with the keyboard. I.e. while you're not in add card mode, you can press "3" to add the third label to the card your mouse is over. So just hovering over all of the cards and pressing 3 over each one will add the appropriate label. So take a look at the keyboard shortcuts (which has its own keyboard shortcut "?"), to see if that works for you.
I've seen this Chrome Extension that does exactly what you want. It costs
US$0.99 per month, though.
I've also, before knowing about the existence of that extension, just wrote Batch Actions for Trello, a standalone website that should be able to perform most of these "bulk" tasks, including "assigning the same member to multiple cards" and "adding the same label to multiple cards"
As of today, there is no way to do that on Trello, which is sad. You have to do that manually for every card you want to assign a label or a member.