You'll get more individual attention with a single person, but unless you're paying a full-time salary, you won't be that person's only client.

CRO work can be billed hourly or by project. For someone really good, you can expect to pay $100-150/hr, probably.

Look for stats.

Not all campaigns are the $300,000,000 button— https://articles.uie.com/three_hund_million_button/ —but showing you stats means that CRO person or agency is doing their dilligence to track their own progress.

YOU should define the goals, not them. But they should definitely be able to explain in great detail how they plan to achieve your goals. No smoke and mirrors. Get specifics.

Be skeptical of promises or guarantees. Be accepting of softer language like estimate, experiment, trial, variable, likelihood, etc.

And to answer your last question, if you have good traffic but few leads, yes CRO is what you need. Good luck! Let us know how it goes.