Looks like your UDK lighting is set to unlit (diffuse only) See on the top toolbar where the cube icon is selected? Select the cube icon immediately to the right of it.
I think he means select a bunch of verts on your low poly, then shrinkwrap it to the high poly object. Then select different verts on the low poly and repeate the process.
It's actually really useful when you select the axis in which you want to lock your "move" in, then press X to lock this axis and spacebar to lock your selection.
Oh also check if the UV is flipped for the missing section. In the Unwrap edit window, go to the Select menu and choose Select Inverted Polygons. Flipped UVs won't bake.
When I open the UVW Mapping, it doesn't let me do it myself, it just goes with whatever its set to, which is either, nothing selected or everything selected.
Sure. I'm using select color range in Photoshop, in the second picture I assigned different colors and you can see the "blended" pixels that don't get selected.
If you want to only push a portion of the mesh, make a selection before adding the Push modifier and that modifier will only act on the selection. You don't need to unweld anything.