Does driving for rideshare count as participating in the operationof the business?

Yes, you are doing work to earn the income.

Yes you are the owner of your own self employment business.  You are in business for yourself.  Use your own info.  The people or company that pays you is your customer or client.  You need to fill out schedule C for self employment business income.  You are considered to have your own business for it.  YOU are the business.