In my understanding, string theory uses one dimenional particles.  Are
there theories of the universe and everything that start with 3
dimensional (or better 4 dimensional) particles?   Why or Why not?

Particles in string theory aren't necessarily 1-D. It also features
2-D vibrating closed loops.

   But the dimensions of the strings themselves aren't the dimensions
of the whole Universe. The strings exist in space of a higher number
of dimensions.

   As for if there are theories with higher dimensioned particles, I'm
sure there are, though not in so-called mainstream physics.

String theory speculates that fudemental particles are not in 3
dimensional space at all but a space of 10 11 or 26.