Dear Jiang,
1. He
joined the army last year. (correct)
He has joined the army. (correct)
He has been joining the army (incorrect) for two years.

either:
He has been in the army for two years.
or
He has been trying to join the army for two years.
(do you see how either meaning could be inferred from the first statement?)
2. Do you see anyone over there? (correct)

Are you seeing anyone over there? (incorrect) It could be correct if you are using
seeing to mean
dating.
Are you seeing someone off? (correct)
Here the meanings of 'see' are different.
3. He is looking well today (correct). If you mean that he looks healthy.

What you are looking at? (correct)
jump, arrive, die belong to words that can't be used in progressive. But there are exceptions. That means they can be used in progressive to indicate repetition and near future past or continuous.
I am jumping. They are arriving. He is dying.
We have all been dying since the day we were born.
They have been jumping like crazy.
They will be arriving in forty minutes.
Does this help?