Your two examples are not equivalent.
"I'm teaching at university"
"I teach at university"
My current job is as a teacher. I do this at the university. There is the slight connotation in the first that you are doing that right now whereas the second example is habitual - you do it Monday to Friday, but not necessarily at the time you are speaking.
"I work in the library every day"
Again, habitual. That's what you do for your job, even if you aren't there right now.
"I am working in the library every day"
You are trying to push the 'habitual' behaviour aspect of the first usage onto this sentence, where it doesn't function.
Better would be to re-use the teaching examples from earlier
"I'm working in the library." or
"I work in the library."
You could use the first as an answer to both "Where are you? What are you doing?" & also "What do you do for a living?"
You can imply habitual behaviour in common speech by using the present tense.
The second example is habitual only & can't be really used to describe what you are doing right now.
As commented by Catija, the first three sentences are perfectly OK and as to the last one, the simple present tense is actually the correct usage.
According to grammar, when you are talking about the future, you should use the present simple in the time (when) clause, not a future form. For example, I'll come when I finish my work. So the correct sentence is:
I want to spend a year travelling when I finish university.
(Reference: The Free Dictionary - the use of "when").
Best Answer
This is used to talk about the past, since you're using the past tense: "finished"
This can be used to talk about a planned future.
Example: "When I finish University, I'll move out."
This means I will move out when (usually the moment) I finish University.
This is present perfect tense. This would be the best option for your situation.
Example: "I'll get a job when I've finished University."
This means I plan to get a job some time after having finished University.
While the second case (finish) tends to point to a short time (often a moment) right after the action (finish University), the third case tends to point to any time after the action, which means it can be 2 years after finishing University.