for your first question, i'm surprised at that because StarAlignment seems to work fine against linear, unstretched images, at least for me. then again my stars are always saturated so that might explain that. there are star detection thresholds in the StarAlignment tool that you can change. i've never had to change it but i suppose the sensitivity control is relevant.
on the 2nd, the LinearFit process can do a pretty good job preparing mosaic panels for merging.