Understanding datasheet audio transformer
First, I guess that the table data for Impedance are given at 1KHz because of the sentence Impedance variation: ±10% @ 1KHz. Am I right?

Perhaps impedance ratio between primary and secondary was measured at 1 kHz. 

Then I guess resistance is simply the electrical resistance of the primary and secondary of the transformer, am I right?

Yes, this makes sense.

Finally, what is the impedance that is given?
This gets a bit complicated. With the resistive source or load specified, a flat frequency response will result over a wide frequency range. Take the case of your data sheet first transformer: 10K primary to 2K secondary. With a 10K source resistance driving the primary, and a 2K load resistance on the secondary, you'll get a reasonably flat frequency response from 300 - 3400 Hz, within 3 dB. In this case, the 0 dB reference point was taken at 1000 Hz. At frequencies lower than 300 Hz, less power will be delivered to the 2K load. At frequencies well above 3400 Hz, AC power delivered to the 2K load drops off too. Sometimes a resonant peak occurs at this top end, especially if source and/or load resistances containing reactance are involved.
Nowhere is transformer reactance mentioned. It will vary over the design frequency range of 300 - 3400 Hz. AC losses due to transformer iron will vary too.

Bear in mind that the manufacturer specifies these transformers for audio use, and not for other applications. So specs refer tightly to this one application.