Hello,
SLEEP operation mode has by default set LPM_CPU_POWER_MODE_FLAG_SLEEP_ON_EXIT flag. This means, that CPU core goes to sleep again after any ISR finishes. In order to let the core run again, you have to call function _lpm_wakeup_core() inside your gpio ISR.
The operation mode change can be done from any task, there's no connection to initialization of your gpio interrupt. But check the priorities of your tasks, maybe you are continuously switching to the SLEEP mode in a loop.
Regarding the timer component, it's required that you cancel the timer in a task that created it.
Regards,
PetrM