If she is under 30, she can apply for an IEC (often known as a "working holiday") visa.
http://www.cic.gc.ca/english/work/iec/become-candidate.asp
If not, she needs to find an employer in Canada who is willing to offer her a job and apply for an LMIA (cost to the employer = 1000$) in order for...
That's a very unusual request, but it has happened to others:
http://www.canadavisa.com/canada-immigration-discussion-board/fingerprints-after-test-t342406.0.html
It may be that your name/DOB match someone with a record.
Here are the links to the various PNPs, where you can find out eligibility requirements, application criteria, & whether the programs are currently open or not:
http://www.cic.gc.ca/english/immigrate/provincial/apply-who.asp
If you don't meet the RO, and have just been readmitted to Canada without being reported, it would be playing with fire to leave again before meeting the RO.
It's perfectly possible to sell a house in the UK & transfer the proceeds of the sale to Canada without leaving the country.
Your wife will apply for her PGWP, a job offer is not necessary for this.
http://www.cic.gc.ca/english/study/work-postgrad-how.asp
Once she obtains it, and is working in an eligible job, you can then apply for an OWP as her spouse.
No you don't list your husband as a dependant.
BUT, to do so, you will need to show proof of legal separation, & also legal (court) documents proving you have sole custody of your children and the right to take them out of your home country.
Thanks for confirming that.
OP, I agree with Scylla. Unfortunately you & your partner both seem to have misunderstood the visa/work permit options available.
It's absolutely possible for you to apply Outland to sponsor her as your spouse. While she wouldn't be able to work until her PR came...
Photos are only required for you & family members (dependents) immigrating with you. so as a single person, you only send your own photos.
Regarding forms that aren't applicable to your situation, don't send them, don't tick those lines on the checklist,
In addition to Scylla's advice, if you are looking at becoming a PR & settling in Quebec, you'll need to look at the qc skilled worker programme:
http://www.immigration-quebec.gouv.qc.ca/en/immigrate-settle/permanent-workers/index.html
Thanks for the clarifications :). I was not aware that South Africa was one of the countries eligible for IEC.
As far as entering Canada on a visitor visa is concerned, her ties to her home country are actually more important than "ties to Canada". The latter could be a negative in some cases.