How to make file operations like move/delete without mouse in Finder? I was on Windows for a long time and switched to Mac about year ago.
Some things still looks strange and confuses me:


How to remove a file without mouse in Finder?
How to move (cut) a file without mouse in Finder? (Ctrl+X, Ctrl+V in Windows)
How to get common info about several selected files (for example their size)?
How to go back to previous folder in Finder without mouse? (Backspace in windows)
How to open one image and be able to move between pictures with keyboard (without another picture viewer software)?
You can find many answers here:  http://support.apple.com/kb/ht1343

Specifically:

Cut (for cut copy paste, indeed for almost all windows shortcuts that use CTRL simply use Command instead):
Command+X

Move to Trash:
Command+Delete    

Open Get Info Window:
Command+I

Open an aggregate Get Info Window for multiple files:
Option+Command+I

Show Inspector:
Command+Option+I

Get Summary Info:
Command+Control+I

Goto Previous Folder:
Command+[

Goto Next Folder:
Command+]

Quicklook (Preview):
Spacebar (or Command+Y)

As for this "why Apple decided not to do such obvious operations in Mac OS X?" you just need to remember that what you are used to in Windows isn't necessarily obvious, it's just what you are used to.  Everything has an equivalent in OS X, you just need to learn what is different, and eventually you might even come to think that the OS X equivalents are actually more obvious than what you use now (Command+R instead of F5 for Refresh, for example...)