Sorry about the confusion. The new text in the help you cited was made to alleviate some of that confusion. The principal resulting dataset of the align_epi_anat.py script is a new anatomical or epi dataset that is aligned to the other dataset. Your first example shows no -epi2anat option, so the default operation is to align the anatomical dataset to the epi dataset. In the course of doing that, several intermediate operations are performed including motion correction and slice timing correction among others. Those results are not saved by default.

In AFNI, input datasets, such as the input epi dataset in your example, are rarely modified (exceptions are adding markers in manual "talairaching" and the Draw Dataset plug-in). The answer to question 1, therefore, is the epi dataset that is the input is not modified in any way, so there is no reason to change its history (question 2). If you did want to save the motion corrected and slice timing corrected epi dataset, use the -save_vr option. A new *output* dataset will be created with the base name followed by "_vr+orig". This dataset is not aligned to the anatomical input dataset, but should be aligned to the anatomical output with the default anat2epi alignment.

Output datasets do maintain a history of the individual operations including slice timing correction and motion correction. The principal output datasets, the aligned anatomical and/or the aligned epi datasets, contain an additional note in the history with the align_epi_anat.py command with options.

The processing happens sequentially with slice timing correction first, then obliquity transformations, then motion correction, then the alignment of the anatomical to the epi dataset and finally the reverse direction for aligning the epi to the anatomical dataset. The final output combines transformations for obliquity, motion correction and alignment. For the intermediate files, transformations are not combined, which may be an issue for you if you have oblique data.

Hope this clears everything up.