I'm aware of the differences between intra and inter, but I'm not the most savvy about reencoding them after the fact. Is encoding with intra from an inter-coded video the same as if you originally used intra to begin with? Or does it need to be kept as intra from the start to preserve complete images? Maybe I didn't search well enough, but I'm surprised I couldn't find info on this anywhere.
An encoder receives and works upon uncompressed frames and does not know or care about the encoding of the source stream.
To avoid any information loss, you have to set lossless mode. For x264, this is by done by adding
-qp 0 to your ffmpeg command. But for most purposes, strict mathematical losslessness is not required. See What's the difference between "visually lossless" and real lossless and what does this mean for future encodes?