the case 1 i have asked all people in the walkthrough, and i can not teleport her. And when i do mom's event like you help, the abby can not carry the dragon gem. the case 2 where i call her.
For Leanne please check the notes in your phone, does it list anything not done? What do you mean Abby cannot move the gem, she always can?
Do you see in the notes and are all ticked
Needed: Possess the soul (in the relic), Mirror of Souls ✔, Dragon Gem ✔, Dragon Gem Bound ✔, Can Teleport another person ✔, Attuned the Hidden Room for teleporting ✔
For Catherine, in the notes in your phone for "Ross Sisters" does it list " Wait for Catherine at the construction site at midday and call her"
When you are there do you see the event "
Catherine is not here? " at the construction site?
If you cannot work it out post your save I will check and advise but as I note you are missing something for the teleport and for Catherine I would guess it is either the wrong time/place or you have not yet had the agreement with Catherine