That's odd. Because in the schematic you posted earlier, there does not seem to be any shortage of pins if you had used a Nano. This implies that the schematic in that earlier post was not an accurate depiction of your actual circuit.
The schematic was just missing the 8 outputs that go to the MOSFET modules that are connected to my solenoids. The schematic I posted shows all the inputs that are connected to the Arduino and everything on the breadboard where the entire issue of the Negative wires starting to warp, getting too warm, and where I saw some smoke coming out of for a second or two.
There are also 6 outputs that go to a 1.24-inch round display to act as an indicator to show which mode I am using the system in and a few other information I want my program to display so that I don't have to keep my laptop connected to see that info on the serial monitor. The complete system works without any issues. It is just with the analog sensor connected to the system and they issue with the negatives overheating and plastic melting off is happening.
You complained of smoke. In such a case, always include ALL connected devices in your schematic. There's a chance you miswired something on the 'output' side without realizing it which blows stuff up.
So still enough pins on a Nano.
Analogue pins can also be used as digital pins, except A6 and A7.
Leo..
In the above the diagram only the solenoid named C with the 2 MOSFET modules and the sensor circuit were connected along with the buttons. The smoke was observed on the breadboard where there are wires connected at the terminals to power the breadboard which uses the 5V and GND from the Arduino Mega.
I have a Nano Every and after connecting everything except for the sensor all the pins are occupied except for the AREF, RX and TX pins which i obviously cannot use. I was hoping to use the nano only for the entire project as it is small and compact but the lack of ports was the issue. I am going to add a few more components to my system which will require maybe 5 more digital outputs and 3 more analog inputs so Mega 2560 was the best choice.
Yeah, and my suspicion is/was that you somehow made an error in the physical connections and the GND of the servos somehow was routed through the breadboard. Breadboard connectors only start to smoke above a few amperes, which is not something that's attainable by just an Arduino and a couple of switches. Then there would have been smoke in different kinds of places.
Hi,
Have you got back EMF diodes across the coil terminals of your solenoids?
What MOSFET modules are you using.
PLEASE get out pen(cil) and paper and draw a schematic of your complete circuit.
Do you have Mega gnd connected to gnd on the MOSFET modules?
Do you have a fuse in the postive line of the battery to stop the smoke coming out when you have an overload?
Tom... 
In your diagram #46, you still do not show everything - the -ve wire of your top 12v supply, needs to be earthed to your Arduino earth. Also, you do not show what powers the Arduino!
I think it is best to start all over (new Mega) - use LED's via a 1K resistors, instead of those driver boards. Just see if all works then, then add the driver boards again - see at what stage the smoke comes back - if ever.
I know its work, but, we all want to see this circuit working for you!
And remember the flyback diode over the solenoid.
Schematic diagram for driver board
https://forum.hobbycomponents.com/viewtopic.php?t=1872
I will rip everything out and connect each and every component one by one and see where the problem is and if any problem still exists. I think it was a one-off situation as all the components still work in their individual subsystems. So doing everything again would actually help and I will update on what happens.
Hey Tom,
This is exactly what my current system with the solenoids look like. I will rewire everything to see if the issue was with me connecting the positive and negative somewhere by mistake.
We all wish to do that (R.I.P) ! 
HaHa!
but yeah it turned out to be a faulty section on the breadboard which was causing the positive and negative to get connected to the same pins which were causing the issues. But thank you so much for assisting me with these issues and guiding me through everything.
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