What are the grounds of being able to hold rent from an apartment owner if owner has failed to act upon duties by making the surroundings peaceful?

Check out the Michigan Landlord Tenant Handbook Google it and download it from the State of Michigan's website.

I doubt there is any. Keeping surroundings peaceful is a very broad statement. Out on the street or neighboring park? Landlord has no control. Noise neighbors? If the landlord isn't there, it is then up to you to call the police.

The right to withhold rent generally applies to a landlords failure to timely repair problems affecting the habitability of the rented premises, and commonly involves the tenants right to use one months rent every six months to make those repairs. The tenants typical remedy for a landlords breach of the duty to provide peaceful enjoyment of the premises to tenant, is for the tenant to move out. The failure to move out timely may be treated as a waiver of any such remedy. As peaceful enjoyment of the premises, it should also be noted that the landlord's obligations are limited to reasonable measures designed to address known problems. This issue commonly arises in connection with the criminal conduct of third parties that the landlord has no control over.