1. tenses......nightmare...

I know that the present progressive tense can be used to refer to future arrangement.
for example: I am meeting you after 5. pm.

Please imagine that you are in a library and you are searching for a power outlet.
Finally, you have spotted one in front of you, but someone is blocking the outlet.
So you walk up to he or she, and say "I am using the power outlet."

I know if I say "I am going to use the power outlet." is correct, but can I use "I am using the power outlet." instead?

Another case is as follows:

Sean: Is Peter on holiday this week? (this week is not finished yet)

Atom: No, he is working.

Atom: No, he has been working.

I understand the meaning of reply 1, but I do not know the meaning of reply 2 and their difference. May you help me?

2. Re: tenses......nightmare...

Originally Posted by Atom98
I know that the present progressive tense can be used to refer to future arrangement.
for example: I am meeting you after 5. pm.

Please imagine that you are in a library and you are searching for a power outlet.
Finally, you have spotted one in front of you, but someone is blocking the outlet.
So you walk up to he or she, and say "I am using the power outlet."

I know if I say "I am going to use the power outlet." is correct, but can I use "I am using the power outlet." instead?

Another case is as follows:

Sean: Is Peter on holiday this week? (this week is not finished yet)

Atom: No, he is working.

Atom: No, he has been working.

I understand the meaning of reply 1, but I do not know the meaning of reply 2 and their difference. May you help me?
I don't think you can use the present continuous in your first example, even though you want to use the power outlet in the very near future. If someone is blocking it, you would say:

Excuse me, I would like to use that power outlet. Could you step out of the way please?

You wouldn't really use any version of the future tense when speaking to the person blocking the outlet.

In the second example, if the week hasn't finished yet, then it makes sense to day "No, he's working (this week)". However, if he has been working until the time of the question, but perhaps won't be working the rest of the week, then you might be able to say:

"Well, he has been working but I don't know if he still is."
OR
"He has been working up until now but I'm not sure about the rest of the week."

3. Re: tenses......nightmare...

If the other person said, "Is anyone using this?" you might reply "I'm using it in half an hour when my tutor gets here" because you have a plan to use it.

The present progressive, as you know, means you're doing something right now OR that you have plans to do something in the future. Without the future reference, it sounds like you mean right now -- and clearly, since you are not yet using it, it sounds very unnatural to say that you are.

In the situation you describe, you would need to say something similar to either of the following:
Excuse me, I'd like to use that outlet, please.
Excuse me, I was planning to use that outlet. Could you move your books slightly, please?

EDIT: I see I took too long to type, but I found it interesting that both of us modified your sentences to include "Excuse me" and "please." I know we are just talking about grammar, but the words of courtesy are valued and expected in English so you might want to start including them in your sample sentences.

4. Re: tenses......nightmare...

Originally Posted by Atom98
I know that the present progressive tense can be used to refer to future arrangement.
for example: I am meeting you after 5. pm.

Please imagine that you are in a library and you are searching for a power outlet.
Finally, you have spotted one in front of you, but someone is blocking the outlet.
So you walk up to he or she, and say "I am using the power outlet."

I know if I say "I am going to use the power outlet." is correct, but can I use "I am using the power outlet." instead?
No. You could say something like 'Excuse me - I'd like to get to that socket'. If you were in the library with a friend who had popped out to take a phone call*, and a third person came up and started to unplug her laptop, you could say 'Hold on, my friend's using that. She'll be back in a moment' - in which case the present continuous form refers to an ongoing (past and future) use. If - improbably rude - the third person just unplugs yours, you could say 'What do you think you're doing...? I'm using that. (You could strengthen or weaken the first sentence - that's up to you.
Originally Posted by Atom98
Another case is as follows:

Sean: Is Peter on holiday this week? (this week is not finished yet)

Atom: Nn, he is working.

Atom: No, he has been working.

I understand the meaning of reply 1, but I do not know the meaning of reply 2 and their difference. May you help me?
2 sounds strange in that context. But supposing Peter has been unemployed for a while, and Sean comes to the door asking 'Is Peter there?' The response could be 'No, he has been working for the last few days. He's found a job at last.'

b
* Not very likely, I know - but I wish more people did.

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