In this new series we present observations and modelling of spectral lines formed in main sequence star chromospheres (from G0 to M8). in this paper, we discuss the Hydrogen line formations in very active dMe stellar chromospheres. We present the conclusions drawn from our modelling approach to the AU Mic (dM2e) spectrum. Our final model atmosphere is described in the next paper in this series. Here, we investigate the effects of some stellar (T$_{eff}$ v sin i) and atmospheric (turbulence, temperature structure) parameters on the line formation. We found that observations are best reproduced by a chromospheric structure including a constant temperature gradient (in a log(M) scale) in the chromosphere and transition region. We show that a very thin transition region is required to account for the observed Ly$\alpha$ to H$\alpha$ surface flux ratio. Then, to drive the Balmer lines into emission and reproduce the H$\alpha$ and H$\beta$ self-reversal and FWHM, the chromospheric gradient and transition region pressure must be quite high for the most active stars. We put forward a complete set of important constraints on the possible structures of such active region atmospheres from 5,000 K to 50,000 K. Notably we show that: (i) the chromosphere/transition region temperature break zone must be located at about 8,200 $\pm$ $\sim$200 K, implying that there is rather little plasma above this temperature, (ii) the temperature break zone is central to the formation of Lymna and Balmer lines, it should be smooth and contained in a small column mass domain, (iii) the transition region must be very thin and at a high column lass, {\it log (M)} $\sim$ -3, (iv) the temperature break demarcates the temperature domains of formation of Lyman and other Hydrogen series (v) backwarming due to the Lyman and Balmer radiation fields occurs at the top of the chromosphere, (vi) turbulence and rotational broadening have little effect on the line profiles and fluxes, (vii) rotational broadening should not however be neglected because H$\alpha$ self-reversal is a major constraint to the modelling, (viii) the profiles are weakly dependant on the stellar effective temperature whose uncertainties can be neglected in first approximation. Finally, we further compare our results to observations and propose some general properties that could be tested with future observations.
Key words: Stars: Late-type dwarfs - Stars: Chromospheric modelling - Stars: Activity - Lines: formation - Hydrogen lines - Chromospheric and coronal heating