Hello

By default there is a block 'Events of author' but it cannot be coppied on any page because it relates to the profile. And there is no 'My Calendar' block in Events app at all. 

1. So, you can use 'Events of author' block as 'My Events'. It can be added using Developer app -> Pages builder -> select Persons in the left menu -> select View Profile in dropdown -> click with Add Blocks -> create Service block. Edit the block by changing Module field to Events and add the following in the Code field

array (
  'module' => 'bx_events',
  'method' => 'browse_created_entries',
  'params' => array (
    0 => '{profile_id}',
  ),
)

2. Unfortunately there is no way to create 'My Calendar' block without customization in PHP code.

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Best Regards
Anton