Refurbished Dell 7390? ~$250 has an 13" display with relatively small bezels. I think if you want it even smaller, you’d need some mini laptop or a tablet or steam deck. But that has other downsides. And having a device with an full-size keyboard is nice if you want to type / code.
Not under normal circumstances. I had some issues recovering damaged harddisks that had lots of errors and retries and sometimes either the USB adapter or the mainboard SATA would crap out or handle it better. But for normal copying of HDDs, both should copy the exact same data.