In game, the Gene Lab is part of the Gene Tree area. Here at the Academy, the Gene Lab has its own worksheet.
Sometimes switching tabs or resizing can mess up the tree's viewport. Clicking the Resize button should fix it.
Yes. Click on the center node of the tree. From there, you can click the All button to select everything, or Reset to clear it.
No, but there is a wealth of information in the Library which should help you make educated decisions about how to progress in your game. You can also ask other players for their opinions.
Maybe some day, but not yet. That would not be a simple task.
After you have implanted your genes, click on the Review tab where you will see all of your genes filled in. From there you can save.
You have to be signed in and have a cast of crabs associated to your account to be able to save anything.