No. The agent posts only to a LinkedIn Company Page that you administer; personal profiles aren't supported.
Organization ID: enter the page's number, not its name. Open the page in admin view: in linkedin.com/company/12345678/admin/, the ID is 12345678.
Your own LinkedIn app: LinkedIn connects through an app you create in LinkedIn Developers; one-click isn't available. Add the redirect URL from the field help, request the Sign In with LinkedIn using OpenID Connect and Community Management API products, then connect.
Posts rejected with 401: until LinkedIn approves the Community Management API for your app, posting works only for admins of the Company Page linked to the app.
More: connecting integrations and LinkedIn integration.