Does C# 7.0 Work for .Net 4.5

Does C# 7.0 work for .NET 4.5?

Let's go through the features new in C# 7.0:

Tuples: The System.ValueTuple package has a version for the portable-net40+sl4+win8+wp8 profile. That means it is usable on .Net 4.0. (Not sure why dependencies list only .Net 4.5.)
If you wanted to use tuples on even lower versions of .Net, it should still work, as long as you add the code for ValueTuple and related types to your project.
out variables, pattern matching, local functions, more expression-bodied members, throw expressions, numeric literal syntax improvements: All these features are just syntax sugar, so they don't need any new capabilities from the framework.
ref locals and returns: This feature exposes in C# what the framework supported since the start, so no changes in the framework are needed here either.
Generalized async return types: To use this feature, you need a type that has the AsyncMethodBuilder attribute, which is in the System.Threading.Tasks.Extensions package (along with one such type, ValueTask<T>). This package is only supported on .Net 4.5, so for .Net 4.0, you would need to compile the relevant types yourself. (Using await on .Net 4.0 also requires Microsoft.Bcl.Async, but that's nothing new.)

To sum up: All of C# 7.0 should work on .Net 4.5 after installing the required packages and most of it should work on .Net 4.0 too.

In Which .Net Framework Version C# 7.2 is Available

Language features are independent of .Net version (Framework/Core/Standard).

You will need to use a compiler that understands the newer language features. Assuming you're using Visual Studio 2017, you should update to latest version.

What are the correct version numbers for C#?

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.
C# 10.0 released with .NET 6.0 (November 2021). Major new features: record structs, struct parameterless constructors, interpolated string handlers, global using directives, file-scoped namespace declarations, extended property patterns, const interpolated strings, mixed assignment and declaration in deconstruction, async method builders (via attributes) for individual methods, the CallerArgumentExpression attribute for parameters, enhanced #line pragmas.
C# 11.0 will be released with .NET 7.0 (Date to be annonced, already testable). Major new features: file-scoped types, generic math support, auto-default structs, pattern match Span<char> on a constant string, extended nameof scope, numeric IntPtr, UTF-8 string literals, required members, ref fields and scoped ref, raw string literals, improved method group conversion to delegate, warning wave 7, generic attributes, newlines in string interpolation expressions, list patterns

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.

C# 7 .NET / CLR / Visual Studio version requirements

You do NOT need to target .NET 4.6 and above, that is incorrect. To use Tuples, you need the System.ValueTuple NuGet package. Right on https://www.nuget.org/packages/System.ValueTuple/ you can see it says it supports 4.5 and above, and actually, it supports 4.0 and above. And if you want to get crazy, if you create your own System.ValueTuple class that does exactly what that package does, it will work back on .NET 3.5 and probably older too. For "Task-like" types, you also need a NuGet package, https://www.nuget.org/packages/System.Threading.Tasks.Extensions/. This package also works on .NET 4.5 and newer according to its documentation.

Other C# 7 features will just work on .NET 2 and above as they are just syntactic sugar. For example, I just wrote the following in .NET 2.0 and it correctly throws:

static void Main(string[] args)
{
    string test = null;
    string d = test ?? throw new ApplicationException("test");
}

Likewise, int.TryParse("123", out int i); works just fine in .NET 2.0.

I did not test every single C#7 feature, but in general, with the exception of Tuples (and their related features like deconstruction), it should work in .NET 2.0 and above as most of it is just syntactic sugar. That being said, yes you need VS2017 to compile C#7. I'm sure at some point other compilers will support C#7 but not today.

Features I confirmed work in .NET 2.0:

Binary Literals
Digit Separators
Inline out parameters
Using _ to discard out parameters
Local functions
Type based pattern matching if (obj is int i) and case int i:
Constant pattern matching if (i is 2)
Var pattern matching if (i is var j)
Ref returns
Throw expressions
Expression bodied getters and setters
Expression bodied constructors and finalizers

can .NET 4.5 dll work in Visual Studio 2008?

Only SSIS 2014 has the ability to use 4.5 assemblies. You can only use 3.5 assemblies for SSIS 2008 (R2).

.NET Framework 4.8 seems to use C# version older than 7

I used a comment to formulate the answer. I checked the csproj file and searched for LangVersion.

<LangVersion>6</LangVersion>

Removing the line solved the problem.

The language version nowadays is based on the .NET framework version and is not separately specified.

You cannot set the language version in the projects advanced properties, but the setting seems to be respected despite that.

Does C# 7.0 Work for .Net 4.5