will it cause any damage to your eyes if you kept them closed more than a year?

I suppose it depends on why you have them closed. I think blinking would be automatic and keep them from remaining completely closed.

However, if someone loses control over their muscles and can't open their eyes, there is a far greater risk of something going wrong, but I'm not sure it would damage your eyes.

If this is a homework question, you have to look it up yourself. If you have plans of keeping your eyes closed for a year, I don't even know if it's humanly possible.

I know when my mother was diagnosed with brain cancer, she CHOSE not to open her eyes, for whatever reason. She went 6 months barely opening her eyes, but she did occasionally.

..Not necessarily. People have been in a coma for longer, and in the end come out fine, sometimes with Paraplegia, but that is not related toward the eyes.