The images will be aligned in a new subdirectory named 'aligned' in the folder containing the original files. To stack the images, load them (File>Import>Image Sequence), then select Image>Stack>Z Project (yeah, I know that's not intuitive). Select the appropriate responses in the dialog and click 'OK'. A stacked image is created and displayed. Save it (File>Save Image/Slice as FITS.) into your preferred folder. On my PC, the above processes occur quickly with the 8MB binned 2x2 images I usually deal with. I will be curious to know the reason for this. I suspect a bug, because once - ONCE ONLY, and for no apparent reason - I found that on opening the batch solve FITS and TIFF dialog, the files were NOT grayed out and I was able to batch solve them. ASTAP did a great job, solved all 64, and replaced them with the solved versions, complete with WCS info. When I tried to select those output files in the dialog, I found they were, once again, grayed out.

Then I tried loading the solved images into AIJ - and there it turns out that I was misunderstanding the semantics of the Import Image Sequence dialog.

Plate solving online