I'm not sure of the exact problem without trying to reproduce it but this should be bulletproof I think:
After import, to create the map containing the 4 images, do it in 3 stages:
(1) Create an empty map. It will initially be given an arbitrary coordinate system.
(2) Open the map and drag in just the lower left image. Now the map has the coordinate system of that image, including metrics (offsets and scales).
(3) Drag in the remaining images. The CS doesn't change.
Do Merge Images in that map, without changing the coordinate system. That merges at original resolution, using the exact CS of the map.
Second thing. There is no built-in resize transform yet. However, if you want to do it with the default interpolation method (not sure if it is bicubic or bilinear), you can use Merge Images again, but this time, do changes the coordinate system, specifying the new resolution you want in the Local Scale X and Y (without changing anything else).
P.s. You can use Merge Images for the second purpose (resize) even if there is only one image in the map.