@WKATCL Thanks for posting in our Q&A.
For this issue, I will share some information.
Q1: While MDM policies can enforce security measures and manage work-related data on personal devices, they are typically designed to respect user privacy and do not sync personal data to work accounts without the user's knowledge.
Q2: When you use your home computer to access your work account, the policies and practices in place generally ensure that only work-related data and activities are managed and monitored. So, your personal data and applications on your home computer are not synced to the work account system
Q3: The device is not enrolled to intune, there is no MDM profile created for this device.
Q5: It is highly unlikely that any kind of remote control or Mobile Device Management (MDM) in Office 365 environment would be installed on your home computer without your knowledge.
In the above, I shared some information what I know. For the two questions I didn't answer, it is suggested to create an online support ticket to do some check on your specific device. Here is the support link:
https://learn.microsoft.com/en-us/mem/get-support
Thanks for your understanding and hope everything goes well with you.
If the answer is helpful, please click "Accept Answer" and kindly upvote it. If you have extra questions about this answer, please click "Comment".
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.