I would advise the sooner the better. Picking a right moment to come won't really help you. You will have enough hustle when you arrive, not only looking for a job.
To contact Immigration, Refugees and Citizenship Canada (IRCC) by phone from outside Canada, you'll need to use the international phone number: 1-613-944-4000.
It's not for a lawyer but a border officer to make that decision. The lawyer can overpromise you anything. What documents did you get when you left the border? Conditional removal order, BOC?
Yes, you can do anything to boost your score above the cut-off.
You just need to meet the minimum requirements for the class you were invited in, the overall composition of points doesn't matter.
Your case should have been referred to IRB, did you have an eligibility interview with a border officer? Have you disclosed a prior refused refugee claim?
You will just have to wait. No way to really expedite it.
You can send your passports but they won't sent it back abroad to Russia, only within Poland.
But you submit your passports in Russia.