As a first approximation, I don't see how a wavelength of less than 2 Planck lengths could exist. Are there any other limits that would come into play before that?
For example:
Will the energy density cause the photon to turn into a black hole or something like that?
Will the energy of the photon exceed the total mass and energy of the universe?
The principle of relativity guarantees that the energy of a particle may always be boosted to a higher value, e.g. by looking at the same situation from a different inertial system. All the situations with 1 particle and arbitrary allowed energy (any number not smaller than the rest mass times $c^2$: the rest mass of the photon is zero) are physically equivalent.
That's why the wavelength (which is linked to the inverse momentum) of a photon, or any other particle, may be arbitrarily short, whether it's shorter than the Planck length or not. You can't produce a black hole just from one particle because it's fast. You only produce a black hole if a sufficient amount of mass is concentrated within the Schwarzschild radius from the center-of-mass reference frame.
There's a lot of misconceptions in popular science literature about the Planck length as the "minimum distance". The Planck length is only the minimum allowed distance of "proper distances measured in the rest/otherwise-natural frames" i.e. distances within a hypothetical nearly static object, measured at rest. But the wavelength associated with an arbitrary particle is just some difference of coordinates according to any frame and this quantity can't be constrained because of the principle of relativity.
So the answer to both questions of yours is a resounding No:
No, a single particle with a vanishing or low rest mass can never turn into a black hole, regardless of the high energy, high momentum, and corresponding high frequency or short wavelength. You need to collide at least 2 particles of Planckian energies to produce a black hole. What matters is the center-of-mass energy (which is also zero for a single photon).
No, a photon (or any other particle) whose wavelength is comparable to the Planck length carries the energy equal to the Planck energy which is $c^2$ times the Planck mass. The Planck mass is just 10 micrograms or so, extremely below the mass of the Universe. ;-) It's, in fact, 100 times lighter than a mosquito. It's a big energy if you concentrate it to a single particle – which is what particle physicists usually want to do (in their minds) with the Planck energy. But it is a negligible energy relatively to the latent energy of the macroscopic objects and surely the Universe as well.
A possible (short) non-existence argument for a minimum wavelength:
Observer A transmits a photon of "minimum wavelength" towards observer B who is approaching observer A. Due to the relative motion of B w.r.t. A, the photon will be blue shifted to a wavelength shorter than the "minimum". Contradiction.
q.e.d.
The only possible counter argument to this (on the off chance one exists) would amount to that the proximity of the observer's matter interacts with the photon to cause it to shed energy (e.g. via some hypothetical phenomenon akin to Cherenkov radiation). Even that however would only limit the minimum that can be observed in a given reference frame rather than an absolute minimum for it.
OTOH, if the energy gets high enough, the photon could only be observed briefly or indirectly as the very bright flash caused by the direct observer being totally obliterated.
Theoretically, the wavelength could be as small as you want but below the Planck scale, the laws of physics appear to break down.
