All perfect praise be to Allah The Lord of the Worlds and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
First: Wudu` of the one who can`t control the coming out of urine into the urine drainagebag: If he knows the time during which the urine ceases, then he must do Wudu` to make sure that it is valid, then offer prayer immediately. However, if the urine is continuous, then that person has to make a new Wudu` for every prayer just before performing it and anything that comes out ultimately doesn`t alter the validity of the prayer.
Second: As for the impurity carried in that bag, there are two cases:
1-If the person can remove this bag, empty it and clean it before praying he must do so for his prayer to be valid.
Al-Shirbini(May Allah have mercy on him) said, "Prayer of person who carries impurities on his clothes is invalid because purification is basically legislated to glorify the rituals of God; whereas, impurity negates that."{Moghni Al-Mohtajj, V.1/P.404}.
2-If he cannot do so, or if this constitutes much hardship for him then he can pray with it as the Sharia maxim says: "Difficulties demand facilitation."
However, Shafie jurists are of the view that this person must make up for the missed obligatory prayers once he recovers and removes that bag. On the other hand, the Maliki jurists state that he must make up for only the prayer whose time has coincided with removing the bag. Al-Khurashi, a Maliki jurist, said, "If he prayed while carrying the bag ofimpurity, and couldn`t remove, empty or clean it, then he must re-perform only the prayer whose time has coincided with removing the bag."{SharehMokhtasar Khalil, V.1/P.1}.
Therefore, if it is difficult for the person who carries impurities-due to the above condition-be that in a plastic bag or on his clothes to make up for all the prayers that he had missed, then he may take advantage of the Maliki opinion. And Allah knows best.