Firstly, you need to know that Managed Metadata Service can be responsible as a Content Type Hub. Content Type Hub is a location where you can manage and publish content type across site collection, web application and farm. One more terminology you need to know is Content Type Subscriber, which will subscribe to Content Type Hub.
Once you publish Content Type across your SharePoint environment, you need to run Content Type Hub Timer Job and Content Type Hub Subscriber Timer Job.
Back to your environment, you can use one Managed Metadata Service as a centralized managed metadata and provide term & term set across Web application. While you are creating Managed Metadata Service application, you can indicate your Content type hub, such as http://ecm.ict24h.intranet (my web application is used to control, manage all of information regarding Enterprise Content Management) and you will then need to active Content Type Syndication Hub feature in the site collection that you indicate Content type hub.
Make sure you've had the following settings in the centralized managed metadata:
- Consumes content types from the Content Type Gallery at
- Push-down Content Type Publishing updates from the Content Type
Gallery to sub-sites and lists using the content type.
To terms permission perspective, you couldn't access term because you've not had Contributor permission in the Term Store management yet. Check this post out in order to understand managed metadata permission.
One more thing regarding you have a lot of Web applications concerning term store is that you must make sure "This service application is the default storage location for column specific term sets".
For example, I have 2 managed metadata service applications named : Enterprise Managed Metadata and Human Resource Managed Metadata". I want to use separate Human Resource Managed Metadata in order to isolate term store as well as make security for content type. However, I also want to use Enterprise Managed Metadata as a centralized term store and give properly permission in order to add, edit term set & term. To do that, you just set this setting "This service application is the default storage location for column specific term sets" for Enterprise Managed Metadata. Then site collection administrations click Term Store Management link in Site Settings, they will be driven to Enterprise Managed Metadata.
You need to check the following resources: