It is not possible to open a Photos Library in Photos directly on the Time Machine drive, if that is what you have been trying to do.
Photos needs write access when opening a library, and Time Machine is preventing the write access.
To recover photos from a backup of a Photos Library or iPhoto Library, restore this library using Time machine to folder on your Mac or a different volume. (Restore a library from Time Machine in Photos on Mac - Apple Support)
Then open the restored Library in Photos by quitting Photos, if it is running and then double clicking the Library you want to open.
"I get an "x" out photos app icon and an error message that it can't be open in the updated Photos 2.0. Is there a way I can open photos from an older version of iPhoto in the Photos 2.0?"
You can open iPhoto Libraries in any version of Photos, if the version of iPhoto that created the library is iPhoto '09 or iPhoto '11, but not from older iPhoto versions. The older iPhoto Libraries need to be prepared first with the iPhoto Library Upgrader tool (iPhoto '11: About the Library Upgrader).
Do not use the Photos.app on your Time Machine backup to access the older photos. Restore the iPhoto or Photos libraries from the Time Machine backup, then run your current Photos.app installed in your Applications folder to oped the restored libraries.
