Can I have different plans for each business?

Yes. Each business can be on a different plan: one on Free, another on Pro, etc.
In practice:

• There is no requirement that all your businesses be on the same plan.
• For example, you can have your first business on Free and a second one on Pro.
• To change the plan for a specific business, select that business in the selector and go to "Plans & pricing" or "Subscription"; there you'll see the current plan for that business and you can upgrade or downgrade only for that location.

Billing and payment method are managed per business in the billing portal; when you open it, it opens the subscription for the business you have selected at that moment.