Displaying users who click the button
This is quite a complex task your planning – and it's hard to answer in just a few lines of text. I can basically just recommend you have a closer look at the mighty Rules module in combination with the Flag and the Entity reference module. 

Here's just a vague suggestion / outline of how this could probably be done by combining the above modules:


Put a flag 'participate' on content type event users of role 'B' can use 
Define a new content type 'participation' with checkbox/flag 'confirmed / dismissed' and reference the event and the user to it, editable by 'A' users
Make a rule that generates a new node of content type 'participation' and alerts users of role 'A' of a new request
Extend your profile pages' view with the referenced items of content type 'participation'


There is probably different ways to do this – most likely also easier ways than the one described above. And then there is also a more specific module 'Rules link event' that might fit your demands.