How can I make toast notifications stay on screen longer? I occasionally have a toast notification that is too long to read in the given amount of time that it is displayed. Is there any way to change the length of time these notifications display?

Also, is there any way to view these notifications after they are gone?  This would be ideal, like an app or a folder that logs all the toast notifications where I can review them later.
Simple Answer: No, this isn't possible.

Long Answer:

Toasts are built into apps, and are low level. There is no way for 3rd party apps to catch toasts, and there is no way to view them longer.

This could be possible if you made your own custom ROM however.