Please help me creating two domains with DNS and Active Directory

Please help me creating two domains with DNS and Active Directory

Creating multiple domain in AD integrated DNS design is possible. Opt for creating parent-child DNS delegation. To do so you need to change zone replication scope (https://technet.microsoft.com/en-us/library/cc784148.aspx). To make sure you following the correct method, please refer https://support.microsoft.com/en-us/help/255248/how-to-create-a-child-domain-in-active-directory-and-delegate-the-dns.

Coming to your second question, if the AD integrated DNS zone has the same name as the AD domain name, problems occurs with the registration of A records and NS records at the zone root.  Also, one or more of the following error messages may be logged. So it is better to avoid naming like that if possible.

(Event Type: Error
Source of Event: DNS
Category: None
ID: 4011
Date: 6/28/2000
Time: 7:50:13 PM
User: N/A
Computer: MACHINE1

Event Type: Error
Source of Event: DNS
Category: None
ID: 4015
Date: 6/28/2000
Time: 7:50:13 PM
User: N/A
Computer: MACHINE1

The final status code from event 4015, 0x00000b, maps to error "LDAP_ADMIN_LIMIT_EXCEEDED Administration limit on the server has exceeded." 

Event Type: Warning
Source of Event: NTDS Replication
Category: Replication 
ID: 1093
Date: 6/28/2000
Time: 7:33:24 PM
User: Everyone
Computer: MACHINE1

Event Type: Information
Source of Event: NTDS Replication
Category: Replication 
ID: 1101
Date: 6/28/2000
Time: 7:33:24 PM
User: Everyone
Computer: MACHINE1

Function of DNS in an Active Directory:-

DNS is a system for naming computers and network services. It is organized into a hierarchy of domains. TCP/IP networks, such as the Internet, use DNS to locate computers and services through user-friendly names.

DNS provides support for Active Directory Domain Services (AD DS). If you install the AD DS role on a server, you can automatically install and configure a DNS server. 

DNS zones can be stored in the domain or application directory partitions of AD DS. You can also specify in which Active Directory partition to store the zone and, consequently, the set of domain controllers among which that zone's data will be replicated. 

In general, use of the Windows Server 2008 DNS Server service is strongly recommended for the best possible integration and support of AD DS and enhanced DNS server features. You can, however, use other types of DNS server to support AD DS deployment.