Is it possible to create a pair of polarized, polarization-entangled photons? Is there a light source which emits (mostly) polarization-entangled pairs of photons that have a known polarization angle, e.g. a certain angle in relation to the orientation of the source?
Applying filters to pairs of photons with unknown polarization won't do it, because it would break entanglement.
 A: I don't know about sources that emit polarization-entangled photon pairs, but polarization-entangled pairs can be obtained from a polarized source in many ways. 
One example is Spontaneous Parametric Down Conversion (SPDC). Quoting from Wikipedia:

In a commonly used SPDC apparatus design, a strong laser beam, termed the "pump" beam, is directed at a BBO (beta-barium borate) crystal. Most of the photons continue straight through the crystal. However, occasionally, some of the photons undergo spontaneous down-conversion with Type II polarization correlation, and the resultant correlated photon pairs have trajectories that are constrained to be within two cones, whose axes are symmetrically arranged relative to the pump beam. Also, due to the conservation of energy, the two photons are always symmetrically located within the cones, relative to the pump beam. Importantly, the trajectories of the photon pairs may exist simultaneously in the two lines where the cones intersect. This results in entanglement of the photon pairs whose polarization are perpendicular.


If $\mid V \rangle$ denotes a vertically polarized photon and $\mid H \rangle$ a horizontally polarized photon, then at the intersection of the two cones it will be possible to find photons in the state
$$\mid \psi \rangle = \frac 1 {\sqrt 2} (\mid H \rangle \mid V \rangle +  \mid V \rangle \mid H \rangle)$$
(See here for more details)
Notice anyway that, as Mark Mitchison pointed out, in an entangled pair neither photon has a definite polarization. To understand why, consider the state
$$\mid \phi \rangle = \frac 1 {\sqrt 2} (\mid H \rangle \mid V \rangle +  \mid V \rangle \mid V \rangle)$$
This state is not entangled, as it can be written as
$$\mid \phi \rangle = \frac 1 {\sqrt 2} (\mid H \rangle+  \mid V \rangle ) \mid V \rangle$$
So we know that in this state one photon has vertical polarization, while the other is polarized at $45°$. You can easily see that the same trick cannot be applied to the entangled $\mid \psi \rangle$ state: an entangled state is in fact, by definition, non separable.
So even if you know the polarization state of the two photons before the entanglement, the creation of the entanglement itself will destroy any information about the individual polarization of the photons.
