Hi
First, do not use all of the unused part of the SD for data, create a SWAP partition with 256MB size and only the rest for data. Forget ext2, use journaling file system, ext4 is perfect.
This is not enough to mark partition type but you must format it, both data and swap partion. Best is to do it with piCore itself using fdisk, mkfs.ext4 and mkswap commands as root.
When ready, either reboot or use rebuildfstab command as root.
New data partition is not mounted automatically as base system do not need it. Mount, create a directory /tce and reboot.
Now if everything is OK, downloaded extensions will be stored in /tce on the data partition and kept for next reboot.