Check that you've finished Stripe Connect onboarding under Billing → "Get paid by clients". Until it shows as active, card payments on your booking page won't go through.
Members sign in with the exact email or phone number you have on file for them — there's no self-signup. Open the client's profile and check their contact details match what they're entering.
Make sure the notification is enabled in your settings and your automated reminders (SMS → Automated) are switched on, and that the member has an email or phone number on file.