1) If you are urinating on your self 24 hours non-stop you can do wudhu and pray and disregard what happens. However if you have a few minutes of time between each urine, you have to do wudhu and pray as soon as you can without any mustahab.
2) You have to pray and stay connected with God. Even if you don’t have wudhu you can recite Quran without touching the words, you can recite dua, you can listen to the Quran being recited.
3) You don’t need to always be in the state of purity to study religion.
I advise you to see a doctor who can give you medication to treat this issue.