Thanks, and agreed on both. Ownership is the one I'd sort out first, because it's the hardest to fix later.
On your question: I'd pay for a first step, but make it a real piece of the project rather than a test task. On most of my projects that's a fixed-price scoping week. We write down what "done" means for each milestone, sketch the data model and name the risky parts. If we stop there, the client keeps a plan any developer can build from. If we carry on, the first milestone is small and clickable, so you see how someone works within two or three weeks, not three months.
What I'd avoid is an unpaid or made-up trial task. It shows whether someone can code, which was rarely the problem, and says very little about how they handle feedback or a change in scope.
Agree that most bad remote hires fail on things nobody checked before signing rather than on coding ability. The two checks I would put at the top are who owns the accounts and what "done" means.
Ownership is simple to get right on day one: the repository, cloud account and domain should be in the company's name, with the developer invited in. Definition of done takes more effort. A contract that lists hours or features without acceptance criteria leaves both sides arguing later about whether the work is finished.
For a first engagement, a small, clearly bounded piece of work at a fixed price is a good way to test the relationship. You learn how the person communicates, documents and handles feedback, and the cost of finding out is capped. Do you recommend a paid trial task, or going straight into the main project with milestones?