As long as you are not sure that your hand was najis when you touched the mobile phone, you can consider it as tahir. Furthermore, najasah is transferred from one thing to another if the dampness in one of them is transferred to the other. If the mobile phone does become najis, then it cannot be purified again except with water. It is not prohibited to use it while it is najis.
It is prohibited to play any game that is based on competition and was invented to gain money like playing cards or chess even if such playing was without betting.
If it was proven to you that one of the living Marjas is more knowledgeable than the deceased Marja that you used to follow, then it is obligatory on you to switch to the living Marja. If this is not proven to you and you used to follow a religious scholar that satisfied the characteristics of the Marja then you should continue following him.