Can a stored procedure call itself or recursive stored procedure? How much level SP nesting is possible?

Can a stored procedure call itself or recursive stored procedure? How much level SP nesting is possible?

Yes. 

Because Transact-SQL supports recursion, you can write stored procedures that call themselves. 

Recursion can be defined as a method of problem solving wherein the solution is arrived at by repetitively applying it to subsets of the problem. 

A common application of recursive logic is to perform numeric computations that lend themselves to repetitive evaluation by the same processing steps. 

Stored procedures are nested when one stored procedure calls another or executes managed code by referencing a CLR routine, type, or aggregate. 

You can nest stored procedures and managed code references up to 32 levels.