zyggy

All your first quote means is that they want documentes dated since the time your PR was approved. They don't want anything dated before that time.
All they want is some differing forms of evidence that you have a shared life during the period since you were approved for PR. Phone bills in both your name every six months shows that. It shows that you continued to have that shared account during the time period. Same with a credit card.
Each person will have a different types of documents to provide... it is truly unique.. But the documents that they love the most are the following
1) Proof of joint ownership or leasing of property (real or personal) such as house deeds, property tax statements, car titles, car registration documents, etc.
2) Proof of joint financial information (bank statements in both your names, joint credit card accounts, etc)
3) Proof of beneficiary status (having each as a beneficiary on life insurance, 401k's etc. Wills made naming each as executor, medical and financial powers of attorney for each other, etc.)
4) Tax returns filed as married (seperately or jointly) If separately, they both should have the same address.
If you have a few things from each of the first three categories plus the tax returns, you will have little problem being approved either at the SC or during an interview (if you are randomly selected)

It is collected at the POE. If you didn't have the money, they would have had you place it in a bonded warehouse until you did have the money. ...
However, in your case, they probably chose not to collect it...
In the US, CBP's focus is security, not revenue collection.... so they let a lot of duty slide when it's a relatively small amount (less than $1,000 or so) and it's an individual paying... They would rather put their resources out in primary and secondary looking out for bad guys than having officers sitting in secondary filling out reams of paperwork to collect a few hundred bucks in duty...
In Canada, it's a little more the opposite...

It doesn't work that way. If you use NEXUS, your entry is based on the program. You have to go through a regular line and get entered into their system on the visa. Sorry, but you're going to have to wait in line. Just show up to the airport earlier.

Also, the terms of the U.S. Canada Tax Treaty overcome those directions.
The terms are as follows:
1. For the purposes of this Convention, the term "resident of a Contracting State" means any person
who, under the laws of that State, is liable to tax therein by reason of his domicile, residence, place of
management, place of incorporation or any other criterion of a similar nature, but in the case of an estate
or trust, only to the extent that income derived by such estate or trust is liable to tax in that State, either
in its hands or in the hands of its beneficiaries.
1. Subject to the provisions of Articles XVIII (Pensions and Annuities) and XIX (Government
Service), salaries, wages and other similar remuneration derived by a resident of a Contracting State in
respect of an employment shall be taxable only in that State unless the employment is exercised in the
other Contracting State. If the employment is so exercised, such remuneration as is derived therefrom
may be taxed in that other State.
To sum up, income that was earned while a resident of Canada is only taxable in Canada and therefore must be excluded from taxable income in the other state.

Also, the terms of the U.S. Canada Tax Treaty overcome those directions.
The terms are as follows:
1. For the purposes of this Convention, the term "resident of a Contracting State" means any person
who, under the laws of that State, is liable to tax therein by reason of his domicile, residence, place of
management, place of incorporation or any other criterion of a similar nature, but in the case of an estate
or trust, only to the extent that income derived by such estate or trust is liable to tax in that State, either
in its hands or in the hands of its beneficiaries.
1. Subject to the provisions of Articles XVIII (Pensions and Annuities) and XIX (Government
Service), salaries, wages and other similar remuneration derived by a resident of a Contracting State in
respect of an employment shall be taxable only in that State unless the employment is exercised in the
other Contracting State. If the employment is so exercised, such remuneration as is derived therefrom
may be taxed in that other State.
To sum up, income that was earned while a resident of Canada is only taxable in Canada and therefore must be excluded from taxable income in the other state.

Actually she can. You can use the 2555 to exclude the income you earned in Canada, since she would pass both the substantial presence test and the tax home test for the time she was resident in Canada. Canada was her tax home before she entered the US and she has to live in the foreign country for 183 days of the previous 12 months. It is not based on a calendar year basis. Any Foreign income earned after you entered the US to become a permanent resident is subject to US tax. Any foreign tax on that income would be taken as a foreign tax credit using Form 1116.
You need to file a form 8891 for the RRSP. It's an infomation only form.

Actually she can. You can use the 2555 to exclude the income you earned in Canada, since she would pass both the substantial presence test and the tax home test for the time she was resident in Canada. Canada was her tax home before she entered the US and she has to live in the foreign country for 183 days of the previous 12 months. It is not based on a calendar year basis. Any Foreign income earned after you entered the US to become a permanent resident is subject to US tax. Any foreign tax on that income would be taken as a foreign tax credit using Form 1116.
You need to file a form 8891 for the RRSP. It's an infomation only form.

Actually she can. You can use the 2555 to exclude the income you earned in Canada, since she would pass both the substantial presence test and the tax home test for the time she was resident in Canada. Canada was her tax home before she entered the US and she has to live in the foreign country for 183 days of the previous 12 months. It is not based on a calendar year basis. Any Foreign income earned after you entered the US to become a permanent resident is subject to US tax. Any foreign tax on that income would be taken as a foreign tax credit using Form 1116.
You need to file a form 8891 for the RRSP. It's an infomation only form.

First, how is your sister in the US now... has she been in the US since her birth and only now is planning to leave the country? Does she have a Green Card? There are important matters.
The first issue is whether or not your sister is a citizen is based on the law as it existed when she was born... in 1971, NOT today. I believe the law then was 10 years of reisdency not the 5 as it exists now.
The law as it existed in 1971 is summarized as follows:

The person's parents were married at the time of birth One of the person's parents was a U.S. citizen when the person was born The citizen parent lived at least ten years in the United States before the child's birth; A minimum of 5 of these 10 years in the United States were after the citizen parent's 14th birthday. For persons born out-of-wedlock (mother) if all the following apply:

the mother was a U.S. citizen at the time of the person’s birth and the mother was physically present in the United States or one of its outlying possessions for a continuous period of one year prior to the person’s birth. You allude to the fact that her parents were married at the time of birth.
I agree with some of the comments. This is a case where you need to get Congressional representation involved. I would file for the N-600 immediately. Do not let your sister leave the US until this matter is resolved. She may not be able to get back in. Her business travels are going to have to be postponed for a significant period of time.
My guess is that this case is complicated enough and the evidence grey enough that the State Department will not want to touch it. They will likely want the agency that directly deals with Citizenship matters, USCIS, to make the final decision.
This is a case where I would consult with a immigration attorney. He would be able to develop a case that would stand the best chance of success from USCIS scrutiny. Since this is not an open and shut case as far as evidence is concerned, it would be money well spent.
Best of luck