The two 1mH coils in series will get you 2mH so long as they are not oriented w.r.t each other such that their magnetic fields can interact. Why not just go with a 1mH coil and be done with it? If the series resistance needs to match what the 2mH coil had, just pad the resistance of the 1mH coil with a bit of series R as needed.
I have no idea what you're talking about. The diagram you put up is for Tannoy DC2000 speakers, which have a dual concentric driver and, in addition, a separate woofer. The diagram shows a 1mH inductor in series with the LF of the dual concentric, and a 2mH inductor in series with the separate woofer.
If you plan to use two in series it makes sense to take advantage of this. The two 1mH inductors are too large to use in this situation but you could combine one with another smaller one. You end up with a reduced resistance and you can trim the inductance simply over a range.
To keep the dcr low on the series inductors, surely. Pretty standard. If the OP wants to upgrade the parts, though, heavier gauge air core would be the obvious way to go.
The diagram posted by the OP does not have two inductors in series with each other.
Isn't the resistance of the air core inductor in the HF section necessary to the function of the series notch filter?
And just to emphasise once again, there is an iron core inductor in series with each bass driver, but nowhere in the schematic are there two inductors in series with each other.
(That's my emphasis in the above transcription.)
Tubenstein's opening description bears no relation to the Tannoy crossover schematic he provided.
Colour me puzzled as to what he is trying to achieve!
If, by necessary, you mean that the resistance contributes to the damping of the circuit, then yes, it does.. but if by necessary you meant that it has to be resistance in the wire of the coil proper, then no, it doesn't.