- Serving map tiles
Tilestream is nice but if you want to have live maps (showing new OSM data as they happen) you need Apache and mod_tile (I think this is also used in main OSM site). You download OSM extract from geofabrik or anywhere else set up postgresql server. And updating mechanism. And them every time tile is requested it is checked if data was changed in DB and if it was tile is re rendered otherwise it is just returned. DB is updated each minute/hour/day how fast do you want it. You have to use mapnik style with this but Tilemill can export mapnik xml style. A lot of Tilemill styles are also on GitHub.
- Updating OSM Data
iD editor is main OSM editor for beginners and all changes are saved to OSM database as soon as you save them. It can take couple of minutes to see them in map tiles. This is because of caching. But if you use minute planet diffs you get changes as soon as you made them.
The same is true for all other editors (Potlatch, JOSM, Merkaartor). JOSM is used for more advanced editing usually. It has many more tools. Next to Bing there is also "Mapbox Satellite" option for tracing in iD and JOSM. This are images directly from DigitalGlobe. But it is always better to use data from GPS than only tracing images.
For mapping coordination you can use OSM quality assurance
JOSM has many plugins used to speed up drawing. One very useful for Public transport mapping is Public Transport You can drive with a bus and set waypoints each time you are on a stop. Then at home plugins helps you to add stops to OSM. It also eases adding routes. After all of this is in OSM you can see it in Transport style.
For mapping transit GO Sync should be useful. I also tried OSM2GTFS for bootstrapping GTFS but it didn't work for me on Linux. I write something on my own but didn't open source it yet.
- Routing engines
Why would you need 2 routing engines? I'm currently using OTP for my city routing and it's quite nice. It has multi-modal transport routing, pedestrian routing, bicycle routing and car routing. It also uses elevation data in routing if you have them. (You can get them from STRM or similar) OTP is a router for shortes/fastest path and transit. For example:
OTP is a java REST server with Leaflet fronted.
There also exist opensource Android application to access OTP server. It is also on Google Play and you can add your server URL to connect to it.
I think only OTP and Graphserver support OSM and GTFS data and are open source so you can add own data all others doesn't support Transit data.
I think that the type of software you are looking for is called a chart plotter software. There are several solutions used in navigation, where using a laptop is more and more common. I will not list here the solutions using dedicated hardware (AIS/navigation systems for example).
Amongst paying options you have the "best seller" called MaxSea (http://www.maxsea.com/products/software) that includes 3D navigation, waypoints, tides, weather etc... Their competitors include Expedition Marine (http://www.expeditionmarine.com/) used by Volvo race. They basic do the same thing, with small variations of course.
However, you were looking for free solutions. I can list two that I have used sailing, with a preference for the second one.
The first is called SeaClear (http://www.sping.com/seaclear/), which is a Windows based chart plotter. It can connect to a GPS, and be used as a route planner. Raster nautical charts are supported and you can calculate some additional features (time, fuel consumption) according to data you input (wind, currents, tides). Personally, I don't really enjoy the interface, and had some problems with the software freezing and not recognizing my GPS device.
The second solution I proposed in my comment, is Open CPN (http://opencpn.org). It has seen many developments over the last few years, offering a more intuitive interface and more options than SeaClear. You will find a complete list of functionalities on the website, plus there is an active developing community that back the project up. For me the most useful functionalities are the Tide and Current prediction, Route planning with tidal support and autopilot output.
Best Answer
It is certainly possible to do routing and catchment zone analysis in QGIS if you combine it with PostGIS's pgRouting. The learning curve will be rather steep if you are not used to any of these tools.
I have a couple of posts on the topic from installing pgRouting to calculating catchment zones: http://underdark.wordpress.com/tag/pgrouting/
Of course it is possible to intersect the catchment zones with any second dataset (like administrative districts). That should be the easiest part :)