Employment status uncertainty & loose onboarding process

I started working as a delivery person for a small, local pharmacy recently.

Their ad indicated they were hiring part-time, permanent, and didn't indicate anything about contract/independent work. I had a brief, pleasant chat with one of the owners over the phone and was hired soon thereafter.

My orientation was earlier this week. I was not given any sort of paperwork to sign. I am used to filling out forms for tax, direct deposit, etc. when I start a new job, so I thought this was odd, but I figured such things would be forthcoming and didn't fret about it.

All they asked for from me on my first day was to take a copy of my driver's license. In the ad, the employer indicated that they would want to perform a criminal record check. However, there has been no further mention of this since I started.

During my orientation day, one of the owners took me on the delivery route. In addition to regular prescription deliveries, the job involves acting as a witness for patients in addictions recovery programs to verify that they've taken their medicine. This involves direct management of doses of scheduled substances, so there's a reasonably high degree of trust involved in the position. After my orientation day and for the rest of the week, I performed the above duties on my own.

Today I asked my new employer about time sheets and whether they would send me direct deposit forms, and they responded that I am hired as an independent contractor. I responded that I was under the impression I was being hired as an employee and indicated my desire to be hired as an employee, and they didn't directly acknowledge that but indicated we could discuss the topic further. I have not responded yet. (This was all text correspondence).

I've reviewed the CRA's article titled "Employee or Self-Employed", and it seems to me that my relationship to the pharmacy pretty clearly more closely resembles that of "employee".

Essentially, I'm trying to wrap my head around what feels like a bit of a bait-and-switch, or at the very least, a dysfunctional hiring process. I'm really not sure exactly how to advocate for myself here and just want to be as informed as I can before I discuss this further with the employer.

Sorry, I don't have a single clear legal question, but I'll try to enumerate my concerns:

• If I haven't signed anything, in what sense can I be said to be employed at all? They've said I'm an independent contractor, but even independent contractors sign...contracts, right?
• If I'm an independent contractor, what do I have to do to keep things above board myself--do I have to incorporate my own business entity? Is there anything that would make me ineligible for the pharmacy's insurance which supposedly covers independently contracted drivers?
• Does it sound like this business is bending the law, or am I misinterpreting something? If I do not continue to work there, are there ways of enforcing any real consequences for businesses who post such misleading ads? The ad is still up.

Thanks very much for your attention.