Can you use your domain server to automatically distribute an update or software installation, on all other domain computers ? and how can you do it ?

You can use Group policy software deployment services. However System Center Configuratiohn Manager (SCCM) is the most effective and professional way of software installation / deployment and patch managment now a days. Please note SCCM also includes WSUS services.

yes you can , you can install the Server based role or service WSUS , you can add this role from server manager

install

specify the update download location

specify what type (windows XP update , win8 win7 win vista server OS and applicaiton

specify group of Desktops , Laptops , Server 

specify the time to install update.

I agree with Adeel on WUSU.  Windows Server Update Services (WSUS) enables information technology administrators to deploy the latest Microsoft product updates to computers that are running the Windows operating system. By using WSUS, administrators can fully manage the distribution of updates that are released through Microsoft Update to computers in their network...... of cos not to mention SCCM.  

in domain environment you can deploy MS updates automatically to all MS products in the network by configuring WSUS server.

in domain environment you can deploy *.MSI software automatically to all computers in the network by configuring GPSI (Grou policy software installtion).

If you have enterprise and you need one solution you can use MS SCCM.

Regards,

Use Gp Policys

For installation of OS patches you can Configure WSUS and set correct AD Group policies. If you have workgroup environment then you can change registry settings to make your WSUS work.

You can publish application packages using Group Policy and for that you need to have .MSI package. If you dont have .MSI package still you can create them manually. Let me know if you need help on this.

To publish or assign a computer program, you must create a distribution point on the publishing server.

Yes, we can use it. Recommendable suggestion is 

1. Active Directory server use only for User management/Group Policy/ Domain management
2. Software installation from centralized point is possible through WSUS server. You can install WSUS on seperate server and approve recommendable patches to client machines. So it will push the updates on specific window to client machine