Is it permissible for a young man and a young woman to enter into a covenant as a married couple without having a true seclusion (Khalwah) until their marriage contract is officially concluded?

The relation which isn`t based on a marriage contract is forbidden, and entering into a covenant as a married couple is unaccounted for and is from the evil suggestions of the devil.

Is it permissible for a pious Muslim woman to stay with her husband who had quit praying out of laziness?

Quitting prayer is one of the major grave sins that come after disbelieving in Allah, but the wife of such a person isn`t considered divorced, rather, she should exert all her efforts in order to bring him back to the way of Islam. However, if his sin is likely to lure her from the way of Islam, then she had better separate from him by lawful means such as Mokhal`aa (When a wife pays a compensation for her husband in return for divorcing her). Moreover, if she exercises patience, and remains steadfast on her faith, then there is no harm in doing that.

Does touching one's wife invalidate ablution?

Touching the wife according to the Shafi'ee's doctrine invalidate husband's ablution. And Allah Knows Best.

I am a disabled woman who has vaginal discharges and can`t control her urine. Therefore, I combine prayers. Is that permissible?

All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all his family and companions.

According to the Hanbali doctrine, it is permissible for the sick to combine prayers. In your case (Asker), it is better that you delay the noon prayer until a few minutes before the afternoon prayer in order to minimize the time span between the two and perform each alone. In addition, you can do the same with sunset and evening prayers. Finally, we ask Allah to bless you with recovery. And Allah Knows Best.