Is it permissible to perform Hajj on behalf of a grandmother who is unable to do so for health and financial reasons, given that the father is physically unable? And what are the conditions that must be met by the one performing Hajj on her behalf?

If you have performed Hajj for yourself, then it is permissible for you to perform Hajj on behalf of a deceased person or someone who is physically unable to perform Hajj, with no hope of recovery, such as your grandmother. Seek blessings for your grandmother by performing Hajj on her behalf. However, if your father is unable and asks you to perform Hajj for him, then his right takes precedence because he is more deserving of dutifulness. If your father does not ask, then perform Hajj for your grandmother. When performing Hajj on her behalf, you should intend to perform Hajj for her, enter into a state of ihram from the miqat while chanting the talbiyah on her behalf, and perform the rituals as usual. The reward of Hajj will reach her, and her obligation of Hajj al-Islam will be lifted.