1. Media converters changing media type that is used on the link for example you can change your fiber connection into classic RJ45. Splitters are legacy technology which is not really used today they simply split one cable into 2 cables (no you cant connect 2 devices to this). Extenders - cables like cat 5e have their limits in case of length for most popular (copper) cables categories this is 100 meters for someone this could not be enough so they will use extender to regenerate signal and be able to use copper cable on longer distances like 150 meters.
2. I guess because its single point of failure on the link.
3. Some media converters and extenders have support for POE so it should be possible.
