It there a smallest possible wavelength? And if there is, what is that wavelength?
You should rephrase your question to:
"Is there a smallest possible meaningful wavelength?"
Yes, the Planck length would be. Anything below Planck length isn't meaningful. Things become practically pointless after Planck length, indescribable, dimensionless, etc.
With the caveat that this is true for current theories. One of the points of unification or a new theory would be to describe the sub-Planckian realm.
I'm don't think I follow... is there anything smaller than a Planck length?
If there is, it is not describable by current theories. Whatever that is, cannot be described by GR, QM, and so forth.
The following argument may be wrong, but it explains why everybody believes that at the Planck scale ordinary physics breaks down.
Consider a particle with a Compton wave length; this length describes somehow its localization. Consider the gravitation of that particle and its Schwarzschild radius. Now assume that its Compton wave length becomes smaller than its Schwarschild radius. The particle (according to classical GR) would collaps into a black hole.
If you now set Compton wave length = Schwarzschild radius and solve the equation you will get the Planck length.
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