The 1st one it's about an orphan who was raised in a church/an orphanage (if I remember correctly), and one day he received the appraisal skill and found out that the caretaker is a bandit/thief, killed him in self defense and escaped with a lost princess.

The 2nd one it's about the hero who defeated the demon king but got betrayed and went to a town/village to become a nut picker and found a little girl with mind reading ability.

Edit: Found the 1st one, it's Ore no "Kantei" Skill ga Cheat Sugite - Densetsu no Yuusha o Yomi "Tori" Saikyou e

The second one is probably Yuusha No Kawari Ni Maou Toubatsu Shitara Tegara O Yokodoroi Saremashita.

~4400 manga completed
~1700 ongoing...