(1) How is universal care going to reduce the shortage of primary care doctors?
I don't know enough about the reason for the shortage of doctors but I'd go out on a limb and say its probably not because they don't get paid enough.
(2) How is universal care going to eliminate patents for pharma?
It won't, and it shouldn't. Patents for pharma don't preclude successful implementations of universal healthcare anywhere else. There's a perception that in Canada "drugs are cheap" -- prescription drugs administered outside of hospitals largely aren't covered by OHIP. Provinces act as bulk buying groups and negotiate prices with pharma companies. You want to partake in the market, great, let's figure something out. It works surprisingly well. Patents are your temporary monopoly on creating an invention in exchange for sharing it with the world.
(3) How is universal care going to make non-profit hospitals cheaper?
By regulating fees for services, by lowering the price of drugs via negotiation and bulk purchase agreements, by eliminating marketing budgets, by eliminating insurance billing departments and by capping executive compensation. Hospitals and doctors are public servants elsewhere in the world, not elite rockstars who can bill as they so choose. That doesn't mean they're not well compensated.
Oh, and by socializing malpractice insurance. In the US high-cost states OBGYNs pay $85-200K/yr just in medical malpractice insurance. [1] In Ontario it's around $70K CAD.
(4) How is universal care going to eliminate fee-for-service, which has the administrative costs that are the woes of care providers?
By having a single table of rates that apply to everyone. Ideally with a single payer. This makes billing much, much easier.
(5) How is universal care going to reduce healthcare spending?
Everything I indicated above put together. If you want a concrete example Medicare does most of the above (they can't negotiate drug prices, and they're not single payer, and they haven't socialized malpractice insurance) but they're substantially more efficient. Medicare spends 2-5% of the budget on administrative, where private plans spend 12-18%. That's without recognizing some of the other savings I pointed out. [2]
[1] https://equotemd.com/blog/obgyn-medical-malpractice-insuranc...
[2] https://www.washingtonpost.com/news/fact-checker/wp/2017/09/...