1. The flight plan will typically be from the navigation aid associated with the airport direct to the first waypoint on the airway. Often the airport navaid and first waypoint of the airway will be part of a bigger airway. The actual transition from the runway to the airway will be either via radar vectors (headings from the controller to clear you from traffic until he/she can give you a direct track to one of the waypoints on the route) or it will be a SID (standard instrument departure) which is a set of waypoints that transitions you from the runway to the airway.
2. Waypoints can be part of the low and high airways. Radio beacons such as a VOR or NDB (where they still exist) will typically be part of multiple high and low routes while RNAV (GPS) waypoints are more likely to be associated only with a specific route.
3. There is no specific height or width for airways. The width is nominally 0nm, that is you are supposed to do your best to be smack bang on the centre of the route, but there is a tracking tolerance that is to allow for navigation inaccuracies. The tolerance is not to be used to meander around the airway at will though. When you are given headings from ATC you are being taken off the airway. There is no particular requirement to always be on an airway and you may go off it to avoid weather, for more direct routing, or if the controller needs you to, however whatever you do must be in accordance with a clearance from ATC.
Low routes are below flight level 245 around here (Australia) and high routes are above FL245 but as long as you have a clearance there may be times when you are on a high route at a lower altitude or a low route at a higher altitude.
4. It varies. Waypoints are normally no further apart than 200NM but they can be a lot closer, particularly close to the airport.