Although those are cracks, they also certainly look to be locations of road debris impact (gravel, etc, kicked up off the road). The gravel takes the paint off and even scrapes the steel, the moisture which is routinely around the underside gets at it, and corrosion has a good head start. This is particularly apparent in the second photo, which is of the passenger side, before wire brushing. I suspect that this crossmember is the most exposed to this sort of road debris damage; the others are higher and/or not behind the tires.
I don't see how the entire square tube could get so entirely filled with water that bursting due to freezing would be a concern, and if that happened wouldn't the flat sides of the tube bulge? They don't look bulged to me, but even though the photos are good it can be hard to tell from just photos. Bulging at the crack locations could be distortion after
the crack formed, due to bending stress on the tube, rather than anything which happened to cause
the crack; the relatively high stress in this location when the bike rack is in use would also exacerbate the crack. In any case, a couple of drain holes would prevent a recurrence, if water is a concern.
I assume that "angle doublers" would be "angle iron" (actually steel) over the cracks, "doubling" just the lower front corner of the tube. This makes sense, but careful coating before welding (presumably with a weld-through coating in the weld seam areas) and coating (protective paint) after welding would be appropriate to avoid having a more extensive version of the same problem later. Some rolled angle won't fit against the tubing properly (the legs are tapered, so the inside faces are not quite at right angles; also, the corner radius may be too large compared to the tubing corner), so I assume that you would check any angle for fit and consider using a formed angle (if you can find it with a sharp enough bend radius).
In this illustration, the "hot mill product" (typical structural steel) is the type that might not fit, and the "cold finished product" is the cold-formed type that might be better:
From Foll Formed Angle Strength - Samson Roll Formed Products Company - Samson Roll Formed Products Company