Looks like I missed a whole lot of back and forth!

#1 - Most carpet (installed over 3/8inch pad) will finish well against 1/2 inch thick product. When people go to install baseboards before we get there with carpet, we ask them to keep it up 9/16th of an inch. Normally that is the perfect height (doesn't cause the carpet to dive but the boards look like they are sitting right on top of it). Some unusually thick or thin carpets can affect our recommendations though.

#2 - Pad thicker that 3/8inch will cause most carpet to dive down to the tack strip at the edges. It doesn't look nice, so if you want thicker pad you should (as Mr. Coffer says) "Jack" the strip (and the base).

#3 - When tucking carpet to tile or wood, chances are you'll want the tackstrip closer than 1/2inch (probably 3/8 or less) in order to hold the material. Once again it'll depend on the carpet.

#4 - Attaching carpet only to the risers won't be enough. Many people think the decorative stair rods will do the job, but nowhere near. Their own installation instructions will tell you that.
Carpet needs to be installed with strip on stairs (on the treads) to be safe, unless of course you'd rather glue.

#5 - Many carpet companies have traditional looking runners available for installation on stairs. That said, there typically is some "custom" work needed to turn or finish ends. Normally the installer has to cut & fit the product, send it out for finishing, go back and install it.
If you don't want a traditional look, but still want a runner, you can use a broadloom you like. The only real difference to putting in the traditional, is that now the finishing is for the binding of the edges.
We also tend to use a little bit thinner than 3/8inch pad for these jobs because it seems to look better.

#6 - Carpet that is shimmed up to another surface may need re-stretching sooner than another. Depending on how it is done, sometimes there is quite a valley created under the carpet. Eventually it'll droop into this valley, and possibly affect the tension in the rest of the space.

#7 - Alexh, glad to hear you're OK. Lots of people have died on stairs with less of a fall.

Hope this helps.