  A sample of 34 dwarf irregular galaxies in the Local Volume, most nearer than
5 Mpc, has been imaged in the near-infrared (NIR) in J and K_s at CFHT in
Hawaii and OAN-SPM in Mexico. In CFHT images, stars brighter than M_Ks=-7.5
were resolved. In most cases, the resolved population represents less than 5%
of the total NIR flux in K_s. Although exponential at large radii, surface
brightness profiles for the unresolved component flatten in the centres. They
can be fitted across the whole range of radii with a hyperbolic secant (sech)
defined as a function of two parameters: the central surface brightness and the
scale length of the exponential. Isophotal, total, and fitted sech magnitudes
have been calculated for all galaxies for which the unresolved component was
detected, along with semimajor axes. The scale length and the semimajor axes
correlate linearly with absolute isophotal magnitude. The same is true for
colors and the central brightness. More luminous dIs tend to be larger, redder
and brighter in the centre. The Tully-Fisher relation shows considerable
scatter, but residuals are tied to surface brightness. The galaxies appear to
lie in a ``fundamental plane'' defined by the sech absolute magnitude, the sech
central surface brightness, and the HI line-width. The rms of residuals in M_K
is only 0.4 mag, which implies that the plane can be used to evaluate the
distances of star-forming dwarfs. Color-magnitude diagrams are presented for 29
galaxies in which stars were resolved. Most show a finger centered around
J-K_s=1 mag. In some cases, there is a red tail extending to J-K_s=2.5 mag.
(Abstract slightly shortened).
