Hi,
Addressing each of your questions in turn -
1. There are a number of picture viewer type applications for Linux. digiKam, as already suggested, is one such (and a very good app, too). Others to consider include FLPhoto, gThumb, F-Spot, amongst others. When you say 'auto detect', are you meaning that an application runs when you plug your camera in? If so, it's a slightly different question and will depend on your distro and which Desktop Environemtn you're using.
2. as fouldsy says, most cameras these days (certainly those with removeable memory cards) will appear to Linux as USB mass-storage devices, or can be configured as such.
Some cameras use what is known as the 'Picture Transfer Protocol', which should be catered for by the gPhoto library, which add support for a whole host of cameras which don't use mass-storage. You can check you cameras' compatibility by having a look at -
http://www.gphoto.org/
3. A USB card reader will appear as a USB mass-storage device to Linux - so you would just treat it as an extra hard disk drive from which you can copy files. Again, the manner in which such a device is configured / used will depend on your distro and Desktop Environment, so we could do with knowing those to help further.