Re: 1) Many modern languages do implement some Lisp features, but none do so as well as Lisp. I have yet to see a language that mixes functional programming, an elegant and intuitive standard library, meta-programming, and high performance native code incremental compilation in one development environment. E.g. Javascript is full of bizarre quirks and bad semantics, and its REPLs aren't up to snuff yet, even though it has native-code compilers that are up to snuff. Nothing does meta-programming as well as Lisp. LINQ, Caml4p, etc, are ugly hacks compared to Lisp macros which are baked into the compilation pipeline by design.
Re: 2) I think you are mistaken in assuming that programmers using other languages don't extend the language. They do, they just do it with external, ad-hoc tools. A great example is LLVM's tblgen utility, which generates native assembler backends from table descriptions. It has its own grammar, own parser, own set of bugs. You can do this stuff in Lisp within the language. When I was still learning the language, I put together a table-driven assembler for x86-64 in about two weeks (http://code.google.com/p/amd64-asm/source/browse/#svn%2Ftrun...). It uses macros to take instruction descriptions and generate encoding functions which are then compiled to native code by the Lisp compiler. It's simple, it uses the parser built into the language, you can't ever forget to run the external tool, and it's totally integrated into the development environment. One hotkey sequence expands the macro and shows you the result right in your editor. An error in a macro is debuggable with the integrated debugger just like any other code (compare to C++ templates, which are basically impossible to debug except through trial and error). Literally no other metaprogramming feature comes close to Emacs+SLIME+SBCL.
Re: 3) Lisp doesn't have "less context." It just uses words for context rather than syntax. In C, you see curly braces and you know you have a block. In Lisp, you see the word "progn" and you know you have a block. Lisp is, to a degree, a language for people who think verbally rather than symbolically. The signals are all there--it's just that the signals are words.
Lisp is the only language I've ever used (to be fair, I haven't really used Haskell) where I don't feel like the language/development environment is the bottleneck. It's the only one where I don't lose my train of thought trying to remember to remember the idiosyncratic way someone ordered the parameters to an API call, or because I'm stuck writing a few dozen lines of boiler-plate. It and Python are the only language I've used where API's have sensible defaults (Java is absolutely terrible for this) and I'd dare call the standard library "tastefully designed."