Linearity and time invariance
Nothing conclusive can be said about linearity and/or time invariance. 

For linearity one would need at least (!) to know the response of the system to \$A u(t) - A u(t-1)\$. (e.g. \$2 u(t) - 2 u(t-1)\$ could result in (or in something completely different to) \$2 u(t) - 2 u(t-3/2)\$)

For time invariance one needs to know at least (!) the response to \$ u(t-t_0) -  u(t-1-t_0)\$. It can, but does not need to be \$u(t-t_0) - u(t-3/2-t_0)\$. So it is inconclusive either.