The [Flags] attribute should be used whenever the enumerable represents a collection of possible values, rather than a single value. Such collections are often used with bitwise operators, for example:

var allowedColors = MyColor.Red | MyColor.Green | MyColor.Blue;

Note that the [Flags] attribute doesn't enable this by itself - all it does is allow a nice representation by the .ToString() method:

enum Suits { Spades = 1, Clubs = 2, Diamonds = 4, Hearts = 8 }
[Flags] enum SuitsFlags { Spades = 1, Clubs = 2, Diamonds = 4, Hearts = 8 }

...

var str1 = (Suits.Spades | Suits.Diamonds).ToString();
           // "5"
var str2 = (SuitsFlags.Spades | SuitsFlags.Diamonds).ToString();
           // "Spades, Diamonds"

It is also important to note that [Flags] does not automatically make the enum values powers of two. If you omit the numeric values, the enum will not work as one might expect in bitwise operations, because by default the values start with 0 and increment.

Incorrect declaration:

[Flags]
public enum MyColors
{
    Yellow,  // 0
    Green,   // 1
    Red,     // 2
    Blue     // 3
}

The values, if declared this way, will be Yellow = 0, Green = 1, Red = 2, Blue = 3. This will render it useless as flags.

Here's an example of a correct declaration:

[Flags]
public enum MyColors
{
    Yellow = 1,
    Green = 2,
    Red = 4,
    Blue = 8
}

To retrieve the distinct values in your property, one can do this:

if (myProperties.AllowedColors.HasFlag(MyColor.Yellow))
{
    // Yellow is allowed...
}

or prior to .NET 4:

if((myProperties.AllowedColors & MyColor.Yellow) == MyColor.Yellow)
{
    // Yellow is allowed...
}

if((myProperties.AllowedColors & MyColor.Green) == MyColor.Green)
{
    // Green is allowed...
}    

Under the covers

This works because you used powers of two in your enumeration. Under the covers, your enumeration values look like this in binary ones and zeros:

 Yellow: 00000001
 Green:  00000010
 Red:    00000100
 Blue:   00001000

Similarly, after you've set your property AllowedColors to Red, Green and Blue using the binary bitwise OR | operator, AllowedColors looks like this:

myProperties.AllowedColors: 00001110

So when you retrieve the value you are actually performing bitwise AND & on the values:

myProperties.AllowedColors: 00001110
             MyColor.Green: 00000010
             -----------------------
                            00000010 // Hey, this is the same as MyColor.Green!

The None = 0 value

And regarding the use of 0 in your enumeration, quoting from MSDN:

[Flags]
public enum MyColors
{
    None = 0,
    ....
}

Use None as the name of the flag enumerated constant whose value is zero. You cannot use the None enumerated constant in a bitwise AND operation to test for a flag because the result is always zero. However, you can perform a logical, not a bitwise, comparison between the numeric value and the None enumerated constant to determine whether any bits in the numeric value are set.

You can find more info about the flags attribute and its usage at msdn and designing flags at msdn

C# language version history:

These are the versions of C# known about at the time of this writing:

• C# 1.0 released with .NET 1.0 and VS2002 (January 2002)
• C# 1.2 (bizarrely enough); released with .NET 1.1 and VS2003 (April 2003). First version to call Dispose on IEnumerators which implemented IDisposable. A few other small features.
• C# 2.0 released with .NET 2.0 and VS2005 (November 2005). Major new features: generics, anonymous methods, nullable types, and iterator blocks
• C# 3.0 released with .NET 3.5 and VS2008 (November 2007). Major new features: lambda expressions, extension methods, expression trees, anonymous types, implicit typing (var), and query expressions
• C# 4.0 released with .NET 4 and VS2010 (April 2010). Major new features: late binding (dynamic), delegate and interface generic variance, more COM support, named arguments, tuple data type and optional parameters
• C# 5.0 released with .NET 4.5 and VS2012 (August 2012). Major features: async programming, and caller info attributes. Breaking change: loop variable closure.
• C# 6.0 released with .NET 4.6 and VS2015 (July 2015). Implemented by Roslyn. Features: initializers for automatically implemented properties, using directives to import static members, exception filters, element initializers, await in catch and finally, extension Add methods in collection initializers.
• C# 7.0 released with .NET 4.7 and VS2017 (March 2017). Major new features: tuples, ref locals and ref return, pattern matching (including pattern-based switch statements), inline out parameter declarations, local functions, binary literals, digit separators, and arbitrary async returns.
• C# 7.1 released with VS2017 v15.3 (August 2017). New features: async main, tuple member name inference, default expression, and pattern matching with generics.
• C# 7.2 released with VS2017 v15.5 (November 2017). New features: private protected access modifier, Span<T>, aka interior pointer, aka stackonly struct, and everything else.
• C# 7.3 released with VS2017 v15.7 (May 2018). New features: enum, delegate and unmanaged generic type constraints. ref reassignment. Unsafe improvements: stackalloc initialization, unpinned indexed fixed buffers, custom fixed statements. Improved overloading resolution. Expression variables in initializers and queries. == and != defined for tuples. Auto-properties' backing fields can now be targeted by attributes.
• C# 8.0 released with .NET Core 3.0 and VS2019 v16.3 (September 2019). Major new features: nullable reference-types, asynchronous streams, indices and ranges, readonly members, using declarations, default interface methods, static local functions, and enhancement of interpolated verbatim strings.
• C# 9.0 released with .NET 5.0 and VS2019 v16.8 (November 2020). Major new features: init-only properties, records, with-expressions, data classes, positional records, top-level programs, improved pattern matching (simple type patterns, relational patterns, logical patterns), improved target typing (target-type new expressions, target typed ?? and ?), and covariant returns. Minor features: relax ordering of ref and partial modifiers, parameter null checking, lambda discard parameters, native ints, attributes on local functions, function pointers, static lambdas, extension GetEnumerator, module initializers, and extending partial.

In response to the OP's question:

What are the correct version numbers for C#? What came out when? Why can't I find any answers about C# 3.5?

There is no such thing as C# 3.5 - the cause of confusion here is that the C# 3.0 is present in .NET 3.5. The language and framework are versioned independently, however - as is the CLR, which is at version 2.0 for .NET 2.0 through 3.5, .NET 4 introducing CLR 4.0, service packs notwithstanding. The CLR in .NET 4.5 has various improvements, but the versioning is unclear: in some places it may be referred to as CLR 4.5 (this MSDN page used to refer to it that way, for example), but the Environment.Version property still reports 4.0.xxx.

As of May 3, 2017, the C# Language Team created a history of C# versions and features on their GitHub repository: Features Added in C# Language Versions. There is also a page that tracks upcoming and recently implemented language features.