Can a form submission automatically mark a job 'Records Received', and can reminders run on fixed dates instead of intervals?

No to both currently.

Forms don't automatically update a job's status when a client submits one - a staff member needs to update it manually. As a workaround, you can configure a "send form / form received" phase in the job to track this.

Global Auto Reminders only support recurring intervals (e.g. every 7 days), not fixed calendar dates. Both of these have been logged as feature requests.