www.filext.com (the standard site for information on file extensions) says:
.dmg =
Macintosh OS X Disk Copy Disk Image File

.bsp =
- arahnoWare Enterprise Sever 6 BSP Code Editor
- BestAddress HTML Editor Site Project File
- Getic 3D Scene/Model File
- Half-life/TFC/CS Map
- Quake Map
- Star Trek Elite Force Map File
- Steam Source SDK Compiled Game Map File
- Valve Game Map File
and notes:
- This format is also used by a number of other id Software games. It is usually found archived in a .PK3 file which includes all of the subdirectories and other files (e.g., textures, sounds, etc.) necessary to make the map work with the game.

I suggest you find a Mac to handle the .dmg file.
And I suggest you ask the sender of the .bsp files what exactly these files are, then - if you still feel you need to open it - buy the associated program.

Hope this helps.