is it true that linq has been abolished?

Well, one of the primary reasons for introducing LINQ in the first place was to enable .NET developers to query relational databases in a more natural way using .NET code rather than SQL.

So, as a beginner, I agree with Lakshmanan that you should concentrate on the two LINQ technologies. If you're only interested in SQL Server, then LINQ to SQL is easier than EF so I'd go with that.

1. If by LINQ, you mean LINQ to SQL then, no, it certainly hasn't been abolished.

2. The essential difference between the three is that:

(a) ADO.NET works with relational databases at a fairly low level using DataSets, DataTables, DataRelations and native Sql queries and commands to represent the corresponding database entities. It is fast and efficient but requires a lot of code to map query results to C# classes.  

(b) LINQ to SQL, which only works with SQL Server, uses an object relational mapping between .NET classes and database tables. Queries are based on LINQ rather than native SQL (under the hood the former are translated to the latter).

(c) Entity framework (EF) also uses an object relational mapping but instead of querying classes which represent database tables you query a higher level abstraction known as the 'entity data model'. There's also a provider model which enables you to use other databases than Sql Server.

Since EF was introduced, MS have concentrated more on developing it than Linq to SQL. However, the latter continues to be supported because of its ease of use, relative simplicity and good performance.