Are there any legitimate dispensations in Islam for those suffering from mental illnesses like depression or PTSD, that prevent them from performing certain acts of worship such as prayer and fasting?

It is recommended to supplicate frequently and seek refuge in Allah Almighty, and not to surrender to Satan who whispers to abandon duties or commit forbidden acts. Legal obligation (taklif) is contingent upon intellect and ability; intellect is a fundamental condition for the attachment of obligation, and ability is another condition. If intellect combines with ability, then obligation is established. There is no obligation upon one who lacks intellect, like the insane, nor upon one who is ordinarily unable. Consequently, the effect of psychological illnesses on obligation depends on the extent of their impact on intellect and ability, and this effect varies from one illness to another, from one person to another, and from one state to another. The matter may necessitate consulting psychological specialists.