Does sleeping break wudu?

Deep sleep, especially lying down, breaks wudu. Light dozing while sitting firmly on the ground does not, in the majority view.

Does bleeding break wudu?

In the Hanafi school, blood that flows beyond the wound breaks wudu. In the Shafi'i and Maliki schools it does not.

No. Certainty is not removed by doubt: if you know you made wudu and only doubt whether it broke, it is still valid.

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Wudu stays valid until something breaks it. Some things break it in every school of Islamic law; on a few, the schools differ.

Anything leaving the front or back passage: urine, stool, wind, and other discharge from these places.
Deep sleep in which you lose awareness, especially lying down. Light dozing while sitting firmly does not break it.
Losing consciousness: fainting, intoxication or madness.
What requires ghusl, such as sexual intercourse, also breaks wudu.

Bleeding or pus flowing from the body breaks wudu in the Hanafi school (and, for large amounts, the Hanbali); not in the Shafi'i and Maliki schools.
Vomiting a mouthful breaks it for Hanafis; not for Shafi'is and Malikis.
Touching the private parts directly with the hand breaks it for Shafi'is, Malikis and Hanbalis; not for Hanafis.
Skin contact between a man and a woman who could marry breaks it for Shafi'is; for Malikis and Hanbalis only when there is desire; not for Hanafis.
Eating camel meat breaks it in the Hanbali school only.
Laughing aloud during prayer breaks both the prayer and wudu for Hanafis.

Follow the school you were taught, or ask your local imam.

Eating or drinking (apart from the Hanbali view on camel meat).
Cutting hair or nails.
Looking at something, or seeing your own private parts.
Doubt: if you are sure you had wudu and only doubt whether you lost it, your wudu stands.