As a short answer to your questions:

1. If you mean the "current lines in the homogeneous model", the lines converge in a valley and vice versa (usually it is the case, especially in rugged topographic conditions). Obviously, the more conductive the subsurface is, the shallower the current lines tend to disperse.

2. In the past, "topography correction factor" would be used i.e. Fox et al. (1980) method. Brief description of this method is provided by Giao et al. :

doi:10.1016/j.jappgeo.2008.03.004.

However, with the inverse modeling algorithms, the topography is incorporated into the inverse modeling approach. In the Res2dinv software for example, after discretization of subsurface model into a number of cells, the nodes are shifted in the Z-direction to incorporate the topography.

Please clarify the method you use. You use ERT or VES in your investigation? I think that "You probably use a wrong term".

The mentioned point for "question 2" is related to 2D tomography / ERT.

On the whole, i don't think that your mentioned facts would be OK. Look at a more reliable reference.

In my opinion if the slope is constant along the profile it will not affect the measurements, as long as gravity does not have influence in the current flow and consequently on the electric potential isolines. But if the slope changes along the profile it will affect the measurements as the electrodes are stick on the surface of the Earth at fixed intervals but their true distances will not be the same through the earth in which the current flows.

As regards the second question I agree wit the previous answer given by Seyyed Reza Mashhadi. The inversion programs automatically make the corrections of the differences of the distances between the electrodes along the surface of the earth to their true distances within the earth.

Sure, the topography is more effective on the electric current penetration especially at the slopes parts of the profile. So you can show that at the depth of penetration.at these parts.

I agree with Fernando, it depends on the slope in my opinion: a constant slop especially small ones won't affect much your ERT results yet if it changes significantly (e.i. high angle or terraces with steps), it will definitely have an impact.

The irregularity in topography in all resistivity measurements disturb the current. try to measure in the nearly flat area to minimize current disturbance