What should a person, who doubts the validity of his Wudu, or over performs it, do?

One who doubts the validity of his/her Wudu while performing it should redo it until he/she is certain of having attained purity. But, if doubt was after having performed Wudu, then he/she should not pay attention to that as doubt after the end of an act of worship does not count. This is of course in case doubt was within the reasonable limits since once it goes beyond that, it becomes a whispering of the Shaytaan (devil) which he/she should ignore as the Wudu is valid.

I work for a company whose manager refuses to allow employees to leave during work hours. Do I incur sin if I secretly went out to join the congregation at the Masjid? Is doing so considered a breach of trust?

Praise be to the Lord of the Worlds.

We recommend that you pray at work to encourage your colleagues to follow suit, because whoever guides to good has the like of the reward of the person who actually does it. And Allah The Almighty Knows Best.

Is it permissible for a person who broke fasting in Ramadan because of being sick to pay a ransom?

If there is hope for him/her to be cured, then he would be required to make up for the missed fasting days when he/she recovers, and no ransom is due on him/her. If his/her disease is incurable, then he/she would be required to pay a ransom for each missed fasting day, which is (600) grams of wheat, or rice. And Allah Knows Best.

Is it permissible to slaughter one animal as a sacrifice and an Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth)?

It is impermissible to do so since each of them is slaughtered for a different reason.