This camera can initiate recording up on motion detection. You can even define regions where you want to detect motion. It can also idetify dogs in motion.
Storage location can be on remote NAS or similar server where you need run any IP camera stream capture SW. In my case, I use Synology NAS where it supports recording up to 2x such cameras with a free licence. You can also record continuously and mark on top motion detected time sequences...

Following a character in motion yes. Put on an FTP server of your choice not sure. It can store locally on micro sd card. Paying cloud storage, NAS storage via RSTP.