Random tidbits about the Pekoyama Dojo
Peko was adopted by the Pekoyama Dojo
Peko reminiscence about her parents taking her to an old amusement park.
Because Peko was abandoned as a baby by her birth parents, it can be deduced all her memories regarding her parents is with her adoptive parents.
The only time she feels like smiling outside her Free Time Event, is when she is at an amusement park.
Because Peko was given the Pekoyama's family heirloom, and the obvious fact she bares the family name, you can infer that Peko's adoptive parents was from the Pekoyama Dojo on the Kuzuryus behalf.
Peko states that her dojo is not exactly a Kendo dojo. The fact that their family heirloom bears the symbol of the Kuzuryu clan mascot, the Pekoyamas were mostly likely a vassel family who served the Kuzuryus (I think the Japanese term is Kashin but don't quote me on that)
Peko's experiences at the Dojo
Just because it would be too much to screenshot, it's strongly implied that everything she did was a form of training. Peko can't take an activity at face value and see everything as a form of training. Examples include: Splitting watermelons, dropping coconuts, watching movies, going into haunted houses.
You could make the argument, because Peko was a 'tool', this was the justification to allow Peko to do normal activities.
Overall, Peko recalls only nice things about the dojo
As always, shout out to Peko's pet finch that probably hated her
Not canon in the slightest, but a moment from the manga
Mentions of Peko's childhood that may or may not be related to the dojo