Hello Deepak,
Check if the Owner of the Mailbox have (in their allocated role) permissions to create activities and queue items.
Open queue settings and there should a drop down “Convert Incoming Email to Acitivites” under Email Settings section.
Select “All email messages” option from that dropdown. Looks like you have currently got “Email messages from CRM Leads, Contacts and Accounts”
Regarding your case always getting routed to O365 team, Please ensure to Select "Dynamics 365" while creating the case.
You can follow the below mentioned steps to reach Technical Support By creating a New Support Request by following the below mentioned Steps:
Login to https://portal.office.com
Go To Admin Center
Under Support Click on New Service Request
Select Dynamics 365
Under Identify the Issue Select Relevant "Feature" and "Symptom"
Enter Issue Summary and Provide Issue Details
Click Next -> Yes, Continue
Is your Service Unavailable
How Many Users Afftected
Enter an email address of someone affected by this issue: (I would Suggest email address of Admin User who is available to troubleshoot depending on the timezone from where the Service Request is created)
Click Next -> Provide the Contact Number.
According to the Cloud Solution Provider Frequently Asked Questions Document, the
Initial response times (IRT) depend on the severity of the incident submitted. The severity of
an issue is set by indicating business impact when you submit the SR.
Initial response for technical break/fix incidents, defined by Business Impact:
• Critical Impact (Sev A): 2 hours
Significant loss or degradation of services. Production services down
• Moderate Impact (Sev B): 4 hour
Moderate loss of degradation. Production services partially impacted
• Minimal Impact (Sev C): 8 hour
I hope this helps.
Thanks.