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There are some strongly typed Forths --- although I've never seen one that was out of prototype. Here's one I had a brief look at:

http://www.arestlessmind.org/2009/02/03/intro.html

Of course, since Forths are built around a REPL, to do type checking you need to keep the type objects around at run time, so it may not be suitable for very small systems.

Yes, but they are not conflicting in the sense that they are competing to serve the same purpose.

For exploratory programming, dynamic type systems are nice. For building reliable long-running systems or ones where failure is extremely costly, I like static.

Yes. For example, the powerful "transducers" concept from Clojure essentially cannot be represented in the Haskell type system.

Here's an attempt: http://hypirion.com/musings/haskell-transducers