What documents does a dual US-Chinese citizen need to enter Canada and the US?

First, can I travel to my home country without a US passport, but with my Chinese passport?

Yes you can. Canada doesn't do exit border control, so you just have to show the airline that you'll be let into China. At Chinese border control, just show your Chinese passport.

Secondly, can I go straight to Canada from China without going back to the US, and enter with my Chinese passport, enhanced drivers license and other documents as a proof of citizenship in the US?

As stated in Timatic, the database used by Airlines:

• Passport exemptions: Nationals of the USA with a recommended proof of citizenship such as a:

• US birth certificate; or

• US certificate of citizenship; or

• US certificate of naturalization.

So present your US certificate of naturalisation (alone) at check-in in China (in case of ignorant staff, ask them to check Timatic) and the Canadian border. At Chinese (departure) border control, use your Chinese passport. If they wonder how you're getting into Canada, Show your US certificate of naturalisation

Last, do I need to apply for a US passport after school in Canada before being allowed to re-enter the US, or I can enter with my enhanced drivers license and other documents?

Your enhanced driver's licence alone is fine.

So in summary:

• Check-in in Canada: Chinese passport

• Entering China: Chinese passport

• Check-in in China for flight to Canada: US certificate of naturalisation

• Entering Canada: US certificate of naturalisation

• Entering the US: Enhanced Drivers licence

Important but not really an answer and too big for a comment:

You're dancing on some very thin ice here and you don't realize it.

As user102008 points out, legally you can't have both Chinese and US citizenship--China considers your Chinese citizenship lost the moment you got US citizenship. If you intend to continue this situation you must be very careful that China never finds out that you're a US citizen.

A very important aspect of this is that your passport must look right when you arrive in China. You fly from the US or Canada to China and they'll see you arriving from a country where you need a visa but they won't see the visa in your passport. Oops! Likewise for the return trip--you're not going to be allowed to board a flight to the US on your Chinese passport and if you present your certificate of naturalization you just revealed your US citizenship. Your Chinese citizenship will be void and you're in China without a visa. I wouldn't be inclined to find out what the punishment is.

My understanding of how to work around this is that you must use two air tickets, the intermediate point being a nation where you have visa-free admission on your Chinese passport (so you're not exposed by not having a visa where you should have one.) It must be a separate ticket because the airline will check admissibility when you check in--if you had a single ticket that said China-Japan-USA they would check for transit in Japan (fine) and admission to the US (no visa, you don't get on the plane.) Leave plenty of time between flights because the airlines will not be responsible for a late flight--miss your flight and you most likely have to simply throw away your ticket. Use only your US passport for US-Japan, use only your Chinese passport for China-Japan. (Other countries can be used but the geography favors Japan for this.) Note that this isn't perfect, a detailed examination of your passport will still reveal your deception (as your "stay" in the transit country exceeds the visa-free time.)

Furthermore, the US expects you to enter/exit on your US passport. You can get a US passport in one day on an emergency basis (I suspect your mother being in the hospital qualifies) but this must be done in person in one of a few cities, I don't recall which ones.

And, yes, China definitely checks for this sort of stuff. My wife is China-born but now a US citizen, more than once she's had to prove to the embassy (when applying for a visa) that she has given up her Chinese citizenship.