How to stop Mathematica from deriving index?

This can be solved by applying custom formatting to kx rather than using Subscript:

kx /: MakeBoxes[kx, TraditionalForm | StandardForm] := SubscriptBox["k", "x"];

Then kx will be output as $k_x$, and the derivative will be correct:

D[kx, k]

0

Would highly recommend looking at TagSet (/:) and MakeBoxes in the documentation for further information.

Due to the TraditionalForm used in the MakeBoxes pattern, this will also work with TeXForm:

TeXForm[kx]

k_x

@Roman also suggested Format as an alternative, so to provide some clarification there:

Format[kx] := Subscript[k, x];

By assigning Format[_], the output format of _ can be changed. It's a bit less excessively low-level, as Roman comments. In my own personal experience with Mathematica, it's almost a bit less intuitive, but your mileage will vary. This also works properly with TeXForm.

Regarding OverDot, that is also possible in these cases. For example, with v:

Format[v] := OverDot[v];

Or:

v /: MakeBoxes[v, TraditionalForm | StandardForm] := OverscriptBox["v", "."];