Can SQL Server 2000 and SQL Server 2012 CoExist? We have OLTP Databases on SQL Server 2000 on my client's Prod Server. Planning to create Data Warehouse on the same Server but use SQL Server 2012. Can I install without any issues?
As stated on MSDN side-by-side installation of SQL 2012 with earlier version is supported. However take note of the instance name, if your SQL 2000 instance is a default instance then your SQL 2012 install will have to be a named instance.

I would take note also that some issues may occur with SQL 2000 tools as your SQL Server 2012 installation may attempt to upgrade any shared components it finds. Although I don't know what of SQL 2000 would still exist in SQL 2012.

Now, my opinion and not the opinion of StackExchange, or my dog...I would not suggest configuring a side-by-side install with a SQL 2000 instance. Not knowing the setup, I would highly doubt the server configuration of a SQL 2000 instance is very well suited to what Microsoft suggest for a SQL Server 2012 installation. Especially considering the fact that SQL Server 2012 is only supported on Window Server 2008 SP2 and higher. This all depends on how old the server is and such but just my opinion.