Like enkimute said, your options re translation are exactly the same with matrices and with geometric algebra: either carry a vector offset with you, or move to projective space (homogeneous coordinates).
I'm not sure what you mean. Let Ax mean rotating x by A (which is a rotation matrix, quaternion, rotor, whatever). Then, the composition of Ax + b and Cx + d is
Not with just a rotor (quaternion) and an offset, or with motors (dual quaternions). If you want nonuniform scaling, rotation and translation, then matrices are probably the nicest way to do that.
