Whatever you did to create
/dev/sda2p2, it didn't do what you intended. You created a regular file in memory. In Linux's disk and partition naming convention,
/dev/sda is a disk,
/dev/sda2 is a partition on that disk.
parted output, you currently have three partitions on that disk: a ~300MB partitionwhich is presumably
/boot, a partition using most of the disk space which is presumably the system partition, and a swap partition. The sum of their sizes is equal to the disk size (within the tolerance of the reported approximations), so there is no more space to create other partitions. If you want to create a new partition, you'll need to make room by shrinking one of the existing partitions.
Note that with msdos partitions, you can only have 4 primary partitions, or 3 primary partitions plus 1 extended partition that can contain any number of logical partitions. If you want to create more partitions, you may want to switch to LVM which is a lot more flexible.
Once you've created a partition, run
cryptsetup luksFormat to set up an encrypted volume on it. This volume will be refered to by a name like
/dev/mapper/sda5_crypt. Then, if you want to create a single encrypted filesystem, create a filesystem on the encrypted volume. If you want to partition the encrypted space between multiple filesystems and maybe swap, then make the encrypted volume an LVM physical volume, create a volume group containing this PV, and create as many logical volumes as you like on the VG.