how I should expose the separation negatives
That's going to be a matter of experimentation, I'm afraid. Test strips/sheets, just like when printing onto paper. Because exposure times will be very short, you will probably need to use an ND filter on your enlarger lens.
Either through densitometry or by evaluating prints made from the separation negatives. Both will be a lot of work; the first option a little less so. What you're looking for is a straight (as far as possible) HD curve. You'll need to match the CI to your carbon tissue, sensitization and exposure parameters. Of course you could adjust those as well (mainly through pigment concentration, sensitizer, exposure) so to keep things somewhat manageable you'll have to fix some parameters so you're only left with one or two to adjust. Otherwise you'll go mad pretty quickly.
Lacking a film densitometer you might get somewhere using a scanner combined with a calibrated step wedge.
I've been considering a film-based color separation approach lately myself as well, also for carbon, but frankly I'm not sure if it's going to be a realistic plan. My idea is/was to separate color negatives (typically 35mm or 120, but occasionally 4x5) onto a more affordable panchromatic sheet film stock than TMY2 in 4x5" size yielding separation
positives, and then enlarge to the desired size to create the actual separation
negatives on something cheap & cheerful like single-sided xray film.
I haven't started with this; currently I'm doing it digitally and trying to figure that out. That's already so complex that I wouldn't dream of doing it on film before I figure out a decent workflow with digital negatives. Based on such a digital workflow I think it's slightly more feasible to embark on the film-based approach because you know what kind of issues you're going to run into. It also helps to have nailed other parameters like tissue formulation so that you're not sent off on a goose chase all the time hunting non-film related parameters.
Don't underestimate the complexity of this endeavor. I think there's a good reason why successful color carbon printers are using a digital workflow for the separation part.
If you start work on this, please do keep us updated; I'd be
very interested indeed to hear about your experiences!