REMINDER: I am NOT an expert and I am NOT qualified to offer personal advice.
Nonetheless, question 2 is easy: No, applications for provincial licensing or benefits do not trigger an investigation into a PR's compliance with the RO. Individuals will ordinarily need to present proof of status to reside in Canada, so this can pose a problem for PRs who do not have a current or at least a somewhat recently expired PR card (what needs to be presented varies from province to province).
Remember, the failure to comply with the RO is NOT about doing anything wrong. Neither CBSA nor IRCC will go searching for PRs who have failed to comply with the RO.
That noted, both have a mandate, a duty, to enforce immigration laws and rules, like the PR Residency Obligation. Thus, if and when there is a transaction with either of them that depends on verifying the individual's admissibility as a PR, they will examine the PR for RO compliance if it appears that may be in issue, and investigate further if the initial examination triggers a more formal Residency Determination.
Applying for provincial licensing or benefits does NOT involve any transaction with either CBSA or IRCC.
For Question # 1:
"If the person's overseas wife is willing to applying for a TRV (study visa / visitor visa) so that she can study in /visit Canada, then would that trigger an investigation into RO of the husband who has been allowed to come to Canada AND has not yet applied as well issued a new PR card?"
Since the PR is NOT a direct applicant in this, my understanding is this is NOT likely to trigger a review of the PR's admissibility. So, similarly, no, it will not trigger an investigation into RO compliance.
Other forum participants pay more attention than I do to matters related to applications for temporary resident status, and should be able to offer more information or insight regarding TRVs and such.
Some further observations:
When a PR in breach of the RO "shows up at the POE . . . [the PR] is at the mercy of border agent."
I wince a bit in regards to the use of the word "
mercy" here. The PR is actually far more at the mercy of the facts to that point, many of which the PR no longer has control over but which are largely facts rooted in the PR's past decisions and actions. Especially the fact about how much in breach of the RO the PR is.
CBSA officers are merely charged with the duty of enforcing the rules. Most indications are that neither CBSA nor IRCC play
gotcha games.
Suggesting that PRs in breach of the RO are at the "mercy" of officers when arriving at a PoE is a bit like saying someone driving 160k on the 401 is at the mercy of law enforcement engaged in traffic enforcement. With more similarities than many might apprehend. Big difference, for example, between driving 120k, even though that is significantly above the speed limit, and driving 150k or 160k. Big difference, as well, between going 140k and gaining on a law enforcement vehicle in front of you, and slowing down, versus keeping it at 140k and blowing on by the officer's car. Other factors can very much influence whether the driving pattern will precipitate a traffic stop and being issued a ticket. Is the highway slippery? Is the driver weaving in and out of traffic? Or did the driver otherwise engage in a risky maneuver catching the officer's attention?
PRs who have failed to comply with the RO do not all face the same risks when they arrive at a PoE. And while different officers will vary in terms of their approach, including some more aggressive than others, the facts and circumstances in the individual PR's case will have a big influence on how things go.
Mapping particular factors to how they influence things gets complicated, and can tend toward the highly speculative, but as I often repeat here, the TWO BIG FACTORS are obvious and tend to have much more influence than other factors. They are, again:
-- How much in breach (thus, the sooner the PR gets to Canada, the better)
-- CREDIBILITY, CREDIBILITY, CREDIBILITY!
Of course there are other factors which can loom large in particular cases. PRs regularly coming and going are less likely to attract elevated scrutiny of RO compliance when going through a PoE. PRs who are returning after a particularly lengthy absence are more likely to attract elevated scrutiny of RO compliance. A PR who is returning to Canada after a three year absence is OBVIOUSLY in breach (unless the PR can show one of the credits for time abroad). Among others.