If a photo is removed from photos is it removed from an album it is in also?

Yes

Albums (as events and photos and last "n" months, etc) are not places - they are ways to view photos in the library - remove the photo form the library and it can not be viewed from anywhere since it is gone

You are conceptually not understanding how a database works and you are things of a file based system - iphoto is a database and photos are not duplicated when you organize them

LN

The Note below describes what's affected when a photo is deleted from different locations in the library:

Deleting Photos from an iPhoto Library

1 - from an Event or the Photos mode: select the photo(s) and use the Delete key to move the photos to the trash bin. Then empty the iPhoto Trash bin as follows:

2 - from an album, smart album, book, slideshow, card, etc.: select the photo(s) and use the key combination of Command+Option+Delete to move the photos to the trash bin. Then empty the trash bin as above.

NOTE: deleting a photo from an album, slideshow, book, etc., with only the Delete key only deletes that photo from that item. Deleting a photo from an Event deletes ALL occurences of that photo in the library.

Yes. Do a search for that Keyword at the bottom of the iPhoto window:

When all of the photos matching that keyword are displayed select them all and use the File ➙ New Album menu option.

Or create a new Smart Album with the criteria Keyword is "XXXX".