The credential used to login should have Application Impersonation rights and Organization Management role to access data from Exchange Online.
You can make use of Task Settings step while creating the task, to schedule the Export process to run at specified intervals. The time interval between schedule runs is entirely dependent on the volume of mail transactions.
For example, if the volume/frequency of mails is less, you can create a weekly task, and specify the date range in Item filter conditions as Last Week to export all the mail transactions in the last week. If the volume of mails are high, you can create a scheduled task to run Daily to export all the mail transactions which happened ‘Yesterday’ by specifying date range as Yesterday in item filter conditions.
By default, the E-mail messages will be exported as .eml file, Calendar items as .ics file and Contact items as .vcf file.
Yes. To accomplish this, select New Search Query option in find items and enter a name by clicking on Save this search query button. The query conditions will be saved as a template and you may select this template from Saved Search Queries while creating another task.
You can always get the attachments from the exported .eml files. If you want to save the attachments separately, you can use the settings and naming rules provided in the Attachment Settings step.
The main purpose of using file and attachment naming rules for exporting mails and attachments is for better search capabilities and to avoid duplicate items. Provide a naming rule such that it will be easy for you to find or group mails and also provide Overwrite conditions to handle duplicate items.
To troubleshoot the connection issues while connecting to Exchange Online, verify whether you are able to connect via Outlook Web Access and check for the list of permissions required to view Exchange Online data mentioned in 1st Question.