Is one ablution sufficient for both a missed obligatory prayer and a current obligatory prayer, knowing that there are vaginal discharge that invalidate ablution?

If the discharge is continuous, then it takes the ruling of سلس ( سلس البول - urinary incontinence or سلس الريح - continuous passing of gas, or سلس المذي - continuous discharge of prostatic fluid, or سلس الدم - continuous discharge of blood); a single ablution (wudu') is sufficient for more than one prayer, as long as the time for that prayer does not expire. Or, according to the Maliki school and Ibn Taymiyyah, the ablution is not invalidated by the expiration of the prayer time. However, it is preferable to perform ablution for each obligatory prayer.

As for making up missed prayers, one must hasten to do so at any time. You should make up two or more days' worth of prayers in a single day. Making up one day's prayers in one day is not sufficient, unless you fear hardship, in which case you should make up as much as you can.