Hopefully
@cansha is right. My earlier comments were relevant to both temporary and permanent residence applications. Tbh, no-one here knows for sure but have been involved with applications for people in different circumstances. It comes down to PNP/IRCC rules and how those are applied by the case officer. And it’s certainly true that people with illegal status in some jurisdictions (eg USA) can be successful in coming to Canada.
For what it’s worth...
1. Yes
2. Yes
3. Probably doesn’t matter. The substance of your application and whether you are judged to be legally admissible to Canada is what’s important, not where in the world you are when you apply. The application might end up moving between processing centres if you apply from UK as citizen of Pakistan, ie if they judge it a complex case then will sometimes move between different VACs and Nova Scotia, so might affect processing times. But if you hopefully are successful to get provincial nomination, then you’re looking at it taking at least 6 months after that in any case.
4. Yes, you can apply PNP and EE from anywhere (some PNPs are not for outland applicants, which you can research yourself). It does not matter if you move between countries provides you inform the PNP/IRCC of your new address/job and this doesn’t mean you then don’t meet the conditions (eg you apply stating a certain NOC but actually you’re working in something else in Pakistan, though for AINP it’s your intended NOC in Alberta and then whether you have sufficient recent work experience in that NOC). It might affect the validity of your police certificates and the dates you apply for these, as you’d likely need these for UK and for Pakistan.
As people have said, the most important thing is that you tell the truth. If you did not tell them about your situation in the UK, then they would easily find out ... you’d risk a 5 year ban. Having current illegal status outside of Canada definitely doesn’t prevent you from applying. The UK Home Office aren’t exactly kind or fair to people (said as a British citizen who has plenty of friends on tier 2/4 visas). But all I was saying, which I’m sure you’re thinking about anyway, is that it would likely help if you can restore your legal status in the UK first or have a good explanation of your circumstances. Wishing you good luck with you applications.