1. Yes, if you want to use WP8 features in your WP8 version.
2. Yes, if your application will be useful without any WP8-specific features.
3. No.
4. OS 7.1 for the WP7 version and OS 8.0 for the WP8 version. There are some very limited WP8 features that you can access from a WP7 XAP when running on WP8, such as Windows 8 Tiles (see
Enabling Windows 8 Tiles in Windows Phone OS 7.1 Apps). For most everything else, you'll need two versions. If you don't use any WP8 features (other than maybe Tiles), then you should target OS 7.1 and it can be used on either WP7 or WP8.
5. The link I provided in #4 leads to an example that includes checking the OS version.