  A new "non-standard" quantization of the universal enveloping algebra of the
split (natural) real form $so(2,2)$ of $D_2$ is presented. Some (classical)
graded contractions of $so(2,2)$ associated to a $Z_2 \times Z_2$ grading are
studied, and the automorphisms defining this grading are generalized to the
quantum case, thus providing quantum contractions of this algebra. This
produces a new family of "non-standard" quantum algebras. Some of these
algebras can be realized as (2+1) kinematical algebras; we explicitly introduce
a new deformation of Poincar\'e algebra, which is naturally linked to the null
plane basis. Another realization of these quantum algebras as deformations of
the conformal algebras for the two-dimensional Euclidean, Galilei and Minkowski
spaces is given, and its new properties are emphasized.
