How should someone afflicted with Waswasah (obsessive doubt) deal with the discharge of drops of urine and gas during ablution (wudu') and prayer, especially given that these symptoms occur only during prayer times and cease thereafter, and what should she do when it is not possible to change clothes outside the home?

What you are experiencing is waswasah (whispering from Satan), so ignore it. And whenever Satan deludes you into thinking something has exited, turn away from this delusion. Perform istinja’ (washing after using the toilet) and wudu’ (ablution) normally, then pray.

Even if we assume real drops are exiting, your ruling is that of a person with salis (incontinence). It suffices for you to perform wudu’ once after the time for prayer begins, and you can pray the obligatory and supererogatory prayers with this wudu’. You are not required to change your clothes unless you are certain that impurity has soiled a particular spot. With doubt about something exiting, nothing is required of you.