Good evening,
Would it be economically feasible and engineeringly possible to modify an airplane such as the C172 or C182, modify the wing to add solar panels, add mini wind turbine to the wings, and store a bank of batteries to run such a plane? (Assuming the engine is modified to run on electricity)
I’m confused about the “mini wind turbine to the wings” bit. Are you adding turbines to generate electricity from the air going by? If so, overall, you’ll lose more in drag than you’ll gain from powering the engine so that’s a net energy loss. You don’t want that. Skip that part.
Fitting solar panels to the wings is a bit tricky, and won’t generate a whole lot of power. It’s a lot of effort for something that at most will only reduce the fuel consumption of the plane.
There are solar powered planes, but if you look at one you’ll see how much engineering they had to put into it to get the weight down to a level where the solar panels could provide enough energy to keep it aloft.
This should get you started:
To summarize wiki & some outisde reading …
The current state of the art would not permit retrofitting a heavy, low efficiency airframe like a Cessna to pure electric power.
Some hybrid or fuel cell plus solar power supply driving electic motors can be made to work today for limited missions on specially designed low weight high efficiency airframes.
Pure solar power is almost certainly not practical for ordinary aircraft missions, regardless of the tech involved. The total solar flux, even at 100% conversion efficiency isn’t quite enough. Which is NOT to say that a pure solar-powered airplane is impossible; they exist today. But rather that they will only succeed in highly specialized niche missions. 4-place Chevy-sedan-o-the-skies is not one of those missions.
A LOT of research is ongoing in this area.
You are asking about electrification, not electrocution by the way. At least, you are if you want any repeat business for your airline. 
An electric 172, sure. Here’s one already under development. Battery capacity is still an issue, but there’s a lot of development work underway there, too.
Solar panels, sure, but so far only lighter (unmanned) aircraft, like this one.
Turbine generators to recover tip vortex energy? Sure, it’s just another engineering tradeoff.
The whole combo? Not yet, but it’s not far off.