Does one who suffers from light urinary incontinence or non-constant post-urination dripping have to perform ablution for every prayer? And does he have to perform ablution twice if he wants to make up the Dhuhr prayer before the Asr prayer in the mosque?

The criterion for urinary incontinence ( سلس البول ) is that it is continuous, without interruption for a time sufficient to perform ablution (wudu') and prayer. What the questioner experiences does not fall under the rulings of incontinence. If some urine comes out after ablution and before prayer, he must wash the affected area and repeat the ablution. If he wakes up at 'Asr time and has not prayed Dhuhr, he should pray Dhuhr first, then 'Asr, because observing the order of prayers is obligatory. He is not required to perform another ablution unless his first ablution is invalidated thereafter.