I would like to ask, when in the beginning of a scenario you are given starting Possessions to distribute among the investigators, some investigators have written on their card to start the game with a certain card in hand. Said card is it listed in the starting Possessions or not? Since I tried with Agnes Baker that has written she starts the game with the storms of Spirits spell, and also Jim Culver that starts the game with the golden trumpet unique item and during the game we couldn't decide if it was the one given in the starting Possessions or an extra one (in the case of the spell). Thank you in advance.

Yes all the cards the investigators start with are also listed in the beginning of the scenario. You should give those cards to the correct investigator.