As long as your device uses micro USB it should be fine. The devices that work through the OTG cable will be device specific. Meaning some you will plug in and things like a keyboard will work without any additional software. Some devices require rooting and/or apps like stickmount or nexus media importer. From my experience Nexus devices work pretty well out of the box for things like keyboards and mice. For things like additional storage (USB, SD card) you will need the app.
OTG cables do not have universal mico usb ends.. some fit better than others depending on your device. You may have to try a couple differnet ones to get best fit or buy one someone recoomends for you particular device.
No; there is one USB-OTG standard, all cables should adhere to that standard, so any OTG cable should work with any device that supports the OTG standard. Not all devices with physically compatible connectors support the OTG protocol, and some that support the protocol don't support all types of peripheral devices - for example, a device might support OTG for storage but not keyboards, or vice-versa. The cables are not device specific, but the usefulness of an OTG cable depends on device support.