You went from 10.7 to 10.10 in one jump? Ah, the lovely fallout from upgrades. Factor in that FCP 7 hasn't had any official support since 10.6.8 and things do break.
You can do three things.
1. Create a new USER account. Switch to that account and try to run the tasks in FCP. If they work, you likely have a User Preferences problem with leads us to item #2.
2. Download and run Digital Rebelion's Preference Manager to Trash your FCP prefs. Understand this will delete all custom settings and drive mappings and return your FCP setup to the default state (as it was when first installed). You will need to go into the system to reset any critical ones before use.
3. If Prefs manager doesn't work, you can try deleting the whole FCS 2009 suite and reinstalling. If you go this route, use Digital Rebellion's FCP Remover to do the delete. It gets rid of all the hidden system files as well. Once the delete is complete, reinstall the programs from the original discs and update as required. If you don't have a DVD drive on the computer, find one that does and create disc images to be saved on a portable hard drive. Mount that drive on the target computer, open the images on the desktop and the install will go much faster.
Good luck.
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note: I have no financial interest in Digital Rebellion. I have used these products for years and they work as advertised. Top shelf stuff.