Looking for an understanding of QUOTED_IDENTIFIER i will post some understanding here.

Short version

ANSI demanded that quotation marks be used around identifiers (not around strings). SQL Server supported both:

SQL Server originally:

• SELECT "Hello, world!" --quotation mark
• SELECT 'Hello, world!' --apostrophe
• CREATE TABLE [The world's most awful table name] ([Hello, world!] int)
• SELECT [Hello, world!] FROM [The world's most awful table name]

ANSI (i.e. SET QUOTED_IDENTIFIER ON):

• SELECT "Hello, world!" --quotation mark no longer valid in ANSI around strings
• SELECT 'Hello, world!' --apostrophe
• CREATE TABLE "The world's most awful table name" ("Hello, world!" int)
• SELECT "Hello, world!" FROM "The world's most awful table name"

Long Version

Originally, SQL Server allowed you to use quotation marks ("...") and apostrophes ('...') around strings interchangeably (like Javascript does):

• SELECT "Hello, world!" --quotation mark
• SELECT 'Hello, world!' --apostrophe

And if you wanted a name table, view, procedure, column etc with something that would otherwise violate all the rules of naming objects, you could wrap it in square brackets ([, ]):

CREATE TABLE [The world's most awful table name] ([Hello, world!] int)
SELECT [Hello, world!] FROM [The world's most awful table name]

And that all worked, and made sense.

Then came ANSI

Then ANSI came along and had other ideas:

• if you have a funky name, wrap it in quotation marks ("...")
• use apostrophe ('...') for strings
• and we don't even care about your square brackets

Which means that if you wanted to "quote" a funky column or table name you must use quotation marks:

SELECT "Hello, world!" FROM "The world's most awful table name"

If you knew SQL Server, you knew that quotation marks were already being used to represent strings. If you blindly tried to execute that ANSI-SQL as though it were T-SQL: it's nonsense, and SQL Server told you so:

Msg 102, Level 15, State 1, Line 8
Incorrect syntax near 'The world's most awful table name'.

It is the moral equivalent of trying to execute:

SELECT 'Hello, world!' FROM 'The world''s most awful table name'

Which is like executing:

SELECT 'string' FROM 'string'

You must opt-in to the new ANSI behavior

So Microsoft added a feature to let you opt-in to the ANSI flavor of SQL.

Original (or QUOTED_IDENTIFIER off):

SELECT "Hello, world!" --valid
SELECT 'Hello, world!' --valid

SET QUOTED_IDENTIFIER ON:

SELECT "Hello, world!" --INVALID
SELECT 'Hello, world!' --valid

SQL Server still lets you use [square brackets], rather than forcing you to use "quotation marks". But with QUOTED_IDENTIFIER ON, you cannot use "double quote quotation mark around strings", you must only use 'the single quote apostrophe'.

I saved the following command to a textfile, then executed it with SQLCMD:

SET QUOTED_IDENTIFIER ON
SET QUOTED_IDENTIFIER OFF

Checking in SQL profiler, SQLCMD -i <filename> connects with the following connection options on my system:

-- network protocol: LPC
set quoted_identifier on
...

however the following command issued by SQLCMD when it connects:

SET QUOTED_IDENTIFIER OFF SET TEXTSIZE 4096

and then it runs my script.

So, the answer to 2) is no - running a script with SQLCMD -i is not the same as executing from SSMS (with the default connections options). If a script requires QUOTED_IDENTIFIER ON, then you need to explicitly set it at the start if you're going to execute it this way.