I've played around with a few functional programming languages and really enjoy the s-expr syntax used by Lisps (Scheme in particular).
I also see the advantages of working in a purely functional language. Therefore:
Are there any purely functional Schemes (or Lisps in general)?
The new Racket language (formerly PLT Scheme) allows you to implement any semantics you like with s-expressions (really any syntax). The base language is an eagerly evaluated, dynamically typed scheme variant but some notable languages built on top are a lazy scheme and a functional reactive system called Father Time.
An easy way to make a purely functional language in Racket is to take the base language and not provide any procedures that mutate state. For example:
#lang racket/base
(provide (except-out (all-from-out racket/base) set! ...more here...))
makes up a language that has no set!
.