Mapnik (the default map on the OSM main page) can take a while to update, and not all zoom levels are rendered at the same time.
If you wait a while longer (a day or two), it will probably all look correct. Its also possible you are looking at a cached copy, so worth trying Shift+Refresh in your browser.

You can also mark tiles as "Dirty", which will cause them to be rendered. More details here: osm.wiki/Slippy_Map

For those links in Keepright to work, you need to install the remote control plugin for JOSM, and have JOSM runnning when you click on the link.
osm.wiki/JOSM/Plugins/RemoteControl

What were you doing, and how did you end up with two copies?

Anyway, its easy to delete one of them:
Just open the relation list (Alt+R), select one of them, then click the little bin icon to delete.

It sounds like it is something about how you are using your Garmin. I can mark points in areas just fine on my eTrex Venture Cx.
Move the cursor to the point you want to mark, then press enter. It should give the option of Save / Map / Goto. Choose Save, and it will mark a waypoint there.

I would say if the path is immediately adjacent to the road, separated only by a kerb (eg a sidewalk / pavement), then adding the footway=both/left/right tag to the road is best.

But if the path is more separated from the road (eg with grass in between), then worth mapping it separately. As this means you can show where it actually is, and whether its parallel to the road etc, plus you can tag it with the surface / width / access.
Though if doing this make sure you map where it connects to the road, to help with routing.

The reference number itself may not be copyrighted, but the database may be. see http://en.wikipedia.org/wiki/Database_right and osm.wiki/Legal_FAQ
Yes, it fine to get a road number from a sign etc, but copying a substantial number from a database or other map etc would be questionable (and not allowed in OSM).

I think its quite easy to add OSM maps to the Google Maps API. So then you'd have the choice of using whatever is best for your area, with needing to change much on the website.
An couple of examples: osm.wiki/Google_Maps_Example
http://www.hackvalue.nl/en/article/61/using_openstreetmaps_with_the_google_maps_api

I think it would be useful to have a specific listed building tag. It would make it easy to find all listed buildings in an area.
eg listed_building=grade_A
Probably worth proposing something like that, and/or documenting it in the wiki.

Though what's the copyright status of the listed building register? Worth checking, or getting permission before copying anything from it.

There's more details about Nominatim here: osm.wiki/Nominatim
It does have options for providing some output in XML format etc. Though it says "Currently the details page creates a high load on the server and is only intended as a debugging aide, as a result no xml api is currently provided. Scraping or heavy use is likely to result in an IP ban. "
So maybe not for the lists on that page.

I presume there is a limit on how many streets it lists, which is why it seems to be only A to E? I've checked a few other cities, and they are also partial lists.
Also, the same street listed many times, seems to be because each street is made up of several different ways. This is probably because of where / how the data was imported from. Though there are other reasons to split up streets into separate sections, eg if the speed limit or width changes along the street.

Nominatim can give you a list of features that are within a city / region etc (including streets): http://nominatim.openstreetmap.org/
Search for a place, then click on the "details" link.
The problem is most cities are just mapped as nodes, not areas. So Nominatim has to estimate the area they cover, which is not always accurate.

It looks like that's the case for Barrie: http://nominatim.openstreetmap.org/details.php?place_id=17886

If you know the boundaries of the city you could map it as an area to replace the node, which would improve the Nominatim result.
Also note that Nominatim lists some streets more than once, presumably because they are split into multiple ways.

It says "Port-au-Prince, Haiti" for me.
What language are you using, what is your browser set to?

It looks like Nominatim is getting the country name from this relation: osm.org/browse/relation/307829
Its currently tagged with name:de, name:en and name:fr. If you're not using one of those languages, Nominatim will show the default (local) name tag which is Repiblik Ayiti.
There's also a node for Haiti, which has more languages for the name: osm.org/browse/node/424297281

What exactly do you mean by "import to OSM"?
Do you want to add the objects to the main map database? As you say, OSM is mostly for static / fairly permanent objects. And you should also check the copyright status if importing from elsewhere.

Or do you just want to show a KML file over the top of an OSM map, as an overlay? If so, that's probably easier, you probably want to use OpenLayers.
Start here: osm.wiki/OpenLayers
And also examples here, which includes a few for KML: http://openlayers.org/dev/examples/

Even though that data is "publicly available" on that website, it may still be copyrighted.
That list doesn't appear to have any obvious copyright notice on it. But it seems it is part of this data set: http://badc.nerc.ac.uk/data/radiosglobe/index.html
That says "Please note that the Met Office data sets are available for bona fide academic research only (sorry no undergraduates)"

So probably not allowed for use in OSM (at least without specific permission anyway).

I suppose this depends on the definition of pub. ie does it include hotels / inns with public bars etc. Or restaurants/cafes with bars.

I suspect quite a few of these are mapped in OSM, but are just tagged as tourism=hotel. I think these should be tagged as amenity=pub as well (or with a separate node tagged as a pub).

FWIW, for IV1 113, I mapped those.
Checking my photos, its two postboxes next to another, both for franked mail - one 1st class, one 2nd class (plus another box for stamped mail, with a different ref). Photo here: http://www.flickr.com/photos/vclaw/4089764925/
I'm pretty sure both boxes were IV1 113. Though checking my photos, the ref on one is partially hidden, so it could be different?
IV1 is complete anyway, according to the Dracos list.

Also, I've found that the refs on the Dracos list don't always match what it says on the postbox. A few seem to be swapped about.

(and as for useless descriptions, there's one postbox in IV4 that is only described as "P". I've not managed to find it yet...)

For installing and setting up Mapnik on Ubuntu, I found this article is very useful: http://weait.com/content/build-your-own-openstreetmap-server

Have you tried this EditGpx plugin for JOSM?
osm.wiki/JOSM/Plugins/EditGpx
It might be easier than converting layers etc.

Have you seen this page on the wiki: osm.wiki/Relation:route
It may be the instructions you are missing.
It says the symbol tag is "symbol description - Describes the symbol that is used to mark the way along the route, e.g., "Red cross on white ground" for the "Frankenweg" in Franconia, Germany ".
So not a link (and probably not currently used by any of the renderers).

Also, for roads with multiple refs/names, I think the best option is to use several route relations. ie the way has name=Lawrenceville Highway, but is part of route relations for US 78, US 29 etc. Though I don't know if any renderers will show these (but as TomH says, tag it correctly, don't tag for the renderer).

You can also use the "designation" tag for official rights of way (in England and Wales).
eg designation=public_bridleway or designation=public_footpath etc

See osm.wiki/Proposed_features/Designation

For different language names, use the 2 letter ISO 639-1 code. List here: http://www.loc.gov/standards/iso639-2/php/code_list.php
For Korean, the tag would be name:ko

Also see osm.wiki/Key:name
Scroll down to the section for Localization.