Question: I've a requirement to deploy the below fields using ChangeSets from Sandbox to Production,

I have one field `CaseMode__c` visible to all profiles except two profiles and another custom field, `OffsetHour__c` that should be hidden for all profiles. These fields are available on Case Object.

Can I deploy these permissions with change sets or do I need to do this manually in production?

Answer: 
Since its a custom field include the fields as well as profiles also in the changeset to configure permissions .I would recommend all profiles along with this field in one changeset for deployment with permission same as the source org .
@Ralph : Make sure you have your requirements of having **CaseMode\_\_c** visible to all profiles except two and another field **OffsetHour\_\_c** that should be hidden for all profiles completed in your source ORG.

Now while creating a changeset add all the profiles and the two custom fields in the changeset. This will ensure that all the visibility/permissions related to the two fields will moved to the destination ORG.