  In this article, we conduct a sequential study of possible observable images
of black hole simulators described by two recently obtained rotating geometries
in Einstein gravity, minimally coupled to a scalar field. One of them,
"Kerr-like" (KL), can be seen as a legitimate alternative to the rotating
Fisher-Janis-Newman-Winicour (FJNW) solution, and the other (TSL) is a scalar
generalization of the Tomimatsu-Sato solution. Unlike the previous version of
the rotating FJNW, these solutions do indeed satisfy the system's equations of
motion. Our study includes both analytical and numerical calculations of
equatorial circular orbits, photon regions, gravitational shadows, and
radiation from thin accretion disks for various values of the object's angular
momentum and scalar charge. The TSL solution was found to simulate Kerr for all
valid parameter values with high accuracy. The maximum difference between the
deviations of shadows from a circle for the Kerr and TSL cases does not exceed
1% and fits into the experimental observational data M87*. However,
near-extreme objects show two times smaller peak values of the observed outflow
luminosity of the accretion disk than for the Kerr black hole. The KL solution
cannot be ruled out by the experimental data for small values of the scalar
charge either. As the scalar charge increases, the optical properties change
dramatically. The shadow can become multiply connected, strongly oblate, and
the photon region does not hide the singularity, so it should be classified as
a strong singularity.
