I think most us was trying to drop a hint but sometimes we got to take someone by the hand. With the way it was in the picture I wouldn't be surprised that the new solenoid is toast now due to the short circuit. Unless you got a solenoid shift the second image is nearly useless. Since you are having so much problems doing this either go look at another mower's setup or get someone to help that knows a little more about how to wire the mower.
Probably I am a little blunt here but being hard headed by not asking for local help with in over your head can be costly at times. Most techs are not knowledgeable about electrical wiring. That probably why a third of my repairs are electrical in nature due wiring screw ups. It was good that I spent two years studying electrons back in 77-79 and have the rest of my life working in electronics and electrical industry. It did take a little rethinking when I started seeing DC electrical circuits using AC electrical wiring color code setups. This is why we got to have the actual mower model numbers to lookup wiring diagrams as some manufactures use black (AC electrical) as positive and others use black (DC electrical) as ground (negative).
I had one guy here that listen to others over the net and had replaced his voltage regulator, starter, solenoid, and stator because his mower would not start. He finally brought it to me where I found it was simply a bad terminal at the ignition switch. He was out nearly $300 for a $0.50 terminal.