All my files are on an external HD. When syncing a large folder of 400,000 photos, my LOCAL Mac HD fills up to 100% full of "other" files. Now, my computer does not work again. I have fully reset my Mac 4 times to try to fix this. Any ideas?
Most likely, your Catalog file is on your internal drive (is that correct?) and this means that Lightroom's preview cache is filling up the space.
You can somewhat control the amount of space this preview takes up in Catalog Settings, by changing the size of the previews and also how long the previews are kept.
You can also move the previews to the external HD using something called a symbolic link, but I don't know how to do that, you can search for instructions on that if you want.