...a utility that does this automatically (all operations: *, /, +, -). 

Ooh! sounds nice. Use via command line?

(Sorry to go OT a bit Silver)

a keyframe editor

We called it Retimer. 

1. Convert your animation *.skeleton to *.skeleton.xml using OgreXmlConverter
2. [Open] *.skeleton.xml
3. Choose [Action] and [Value]
4. Press [Run]
5. Change "name=" (if necessary)
6. [Save] it as *.*.skeleton.xml (use a new name if necessary)
7. Convert *.*.skeleton.xml to *.skeleton

Download Retimer

All thanks to Abramoff. 

Remember a discussion before about "cutting" an animation so you can get only the frames you need? Can this tool help with that?  hehe

Yes, of course I remember it and I thought about it. I think you can use the substraction operation and then remove unnecessary frames.
For example, the desired frame begins at 3.13 - this means it must be 0. Use the utility and subtract 3.13 and delete all frames below zero.

You can use Retimer for animation inverting. 

For example, you have "Run" animation.
length="0.8"

Follow these steps:
1. [Action] = "-" ; [Value] = 0,8
2. [Run]
3. [Action] = "*" ; [Value] = -1
4. [Run]
5. Сhange length="0.8"(or not, if you removed the "length check" before)

Voila, you have inverted animation. 

Now thats nice! Now we can make resurrection anims by inverting death anims

Hmm... when I use this tool on the Bloatfang Boss's Special_Eat animation, I get an error saying '0,16667' is not a valid floating point value.I set the Format Float to "0.######" (six pound signs instead of the default five) and tried * and / by 2 for the action. All attempts produced the same error.

When I searched the XML file (using Notepad++) for an instance of "0,", it failed to find any; the comma is likely arising somewhere in the code.

EDIT: The program crashes whenever it tries to handle a floating point number (somehow it seems to be converting decimals to commas).

You must use a point in  Format Float "0.######"
...
And you do not need more than 5# in Format Float. 0.00001 = 10 nanoseconds.

Made sure it had a point there (it does). I only adjusted the float format to six places because the animation had six places, so I erroneously thought it might fix the error.

Here there are some problems in the encodings in different languages. In Russia we always use a comma for Float.

Ah. Assuming this is a C# program (it looks like it easily could be), there should be some locale settings that Microsoft provides that (theoretically) should prevent the need for hardcoded commas. I haven't used them ever, so I don't know how good they are, but I know they exist.
If its not a C# program (it doesn't appear to have a managed assembly, so I still don't know), there might be locale wrappers somewhere by someone, depending on the language used, but I know even less at that point.