There really is no problem using your camera in China, I've been to Beijing and had no problems at all and like wise with more rural parts (check out my blog if you want to see any photos).
However, technically it is illegal to take photos of militarily sensitive areas, this includes things such airports, train stations and possibly police stations etc. and it might not be the best idea to snap away at policemen and soldiers. Although saying this I often saw tourists snapping away whilst waiting for trains with no problems and taking pictures of the soldiers/guards at Tianamen square is fine.
As for taking photos of people it would be good to learn a few phrases in Mandarin and ask people first, although they are not likely to say no from my own experience. but be considerate of the fact that there are still a lot of rural and urban poor that don't want to be stared at by tourists and some people might expect a few Yuan in exchange for a photo. This discretion is particularly true for minorities people such as the Muslim Hui people or Tibetan monks etc., although in some places you might get chased by people asking for a photo to be taken in exchange for some Yuan.
Not sure about tripods, you can probably use them most places as long as you don't get in the way. As for temples and religious buildings there is usually no restrictions, but it can be disrespectful to take photos of the main shrines.
All in all you're not likely to have any problems unless you are a journalist after photos of people who might be victims of government polices!