I can confirm these two points, I did a run with only 1 hired unit (Fairy), and encountered the succubus, slime, tifur, triclops, and ogre girl events. They seem to occur at certain story progression points, so it's either triggered by progress, or by reknown.
Also confirm buying or hiring is not necessary to unlock inventory. In the same run, I bought only my initial set of equipment (4 items), and hired only 1 unit (Fairy as mentioned above). Sold lots of items while exploring dungeons, but all were unlocked and ID'ed via skill. I've now unlocked all the way up to vampiric dagger. This means unlocking inventory can only be triggered by story progression, reknown, or number of transactions (including selling).
Based on this, and what I mentioned above, I think it's quite likely the number of transactions including selling that unlocks shop inventory.