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Below are answers for your questions are below.

Q. I would like to know why all images don't go through all the same processing steps (MPR; GradWarp; B1 Correction; N3; Scaled).
A.The short answer: ADNI Preprocessed images differ in their labels because some manufacturers were able to complete some of the gradient warping and/or inhomogeneity corrections at the time of the scan (as part of the standard product sequences). We believe that all of the ADNI scans have had the appropriate gradient warp and inhomogeneity corrections for the scanner used. Some were completed by the scanner at the time of the scan and some were completed by the ADIRL preprocessing pipeline. The ADIRL only labels the preprocessed scans with the corrections that were applied by the ADIRL.
A longer answer: Every imaging modality is not perfect. Each imaging modality has its own issues that are unique to how the images are acquired.
Some of the correctable issues with MRI are, warping of the images caused by the MRI gradient coils and inhomogeneity caused by using multichannel head coils.
Gradient warping. Gradient warping occurs, to some extent, in every scanner. Some models have almost none and some have quite a bit. To deal with gradient warping, to first order, there is are gradient warp corrections: these are coefficients that are applied in each direction. These coefficients are calculated by the scanner manufacturer. Some scanners are able to apply (at the time of a scan) a 2D correction, some can apply a full 3D correction, some cannot apply any correction and some scanners don’t need any correction. For ADNI 1 trial the Gradient unwarping correction was completed by an image processing lab at UCSD. The ADIRL took over the gradient warp corrections for the ADNI-GO and 2 trials.
For ADNI GO/2, the ADIRL evaluates each scan and determines whether each scan has a 2D or 3D gradient warp correction already applied on the scanner. For scans that still need some correction the ADIRL applies the appropriate correction for that scanner model. A “GW” is appended to the filename to show that a gradient warping correction was applied. For scans that do not need any further correction no “GW” is added to the filename.
Since the gradient warping coefficients only take care of the gradient warping to the first order, in ADNI 1, the ADIRL also did some scaling of the human images, using knowledge about the gradient warp of the scanner, from the ADNI phantom, acquired right after human scan. For ADNI 1 subjects that had an appropriate phantom scan, the ADIRL would scale the human image. Those images had a “Scaled” appended to the file name. Phantom scaling was discontinued for ADNI-GO/2.
During ADNI 1, image inhomogeneity was corrected by a series of 2 scans that allowed for comparisons of the multichannel head coil and the single channel body coil. Using the correction generated from the 2 B1 scans, the ADIRL was able to correct some of the inhomogeneity of the image and labeled those scans with “B1”. Some sites did not correctly acquire the dual “B1” correction scans. No correction was used for scans where the B1 corrections scans were either not acquired or acquired incorrectly. Some of the scanners were able to complete a similar inhomogeneity correction on the scanner at the time of the scan. These scans did not get the B1 correction applied by the ADIRL. The “B1” corrections scans were discontinued for ADNI-GO/2.
In ADNI 1, N3 (an inhomogeneity correction program) was used to further correct the image inhomogeneity. Those files are labeled with “N3”, in ADNI GO and 2 an additional inhomogeneity correction was added after N3, those files were labeled “N3m”.

Q: Are they comparable even though they didn't have all the same steps, for example?
A: The preprocessing steps completed have given us the best known corrections for gradient warping and image inhomogeneity. All of the preprocessed images will have the appropriate gradient warping and most robust image inhomogeneity corrections we have been able to achieve. We hope this will make the images more suitable for comparison and analysis. Comparing/analyzing the non-preprocessed images are more likely to cause discrepancies in your analyses as some of the non-preprocessed images have had gradient warping correction and/or (some) inhomogeneity correction, some of the preprocessed images have little or no corrections.

Q: Is it still appropriate to conduct an analysis using the pre-processed images, for example, in a voxel-based morphometry analysis?
A: We believe it is not only appropriate but preferred. Using preprocessed images will be the best shot at “a level playing field” in terms of comparing images from different scanner makes/models/coils/software.

Q:Finally, is the combination from ADNI1 and ADNI2 processed images possible, or should I stick to what was said in this topic (http://adni.loni.usc.edu/support/experts-knowledge-base/question/?QID=416
A: The changes in the preprocessing pipelines between ADNI1 and ADNI-GO/2 have not been extreme. That said the acquisition protocols and preprocessing pipelines are different. We do not believe that the compatibility between ADNI1 and ADNI GO/2 has been measured and validated to be equivalent.

Thank you.

ADNI MRI Core