Starter changed, still not runing

Hello
I'm new here and its my first topic. I hope you will not eat me alive

My problem is suchs

1)one day I drived home, parked in garage and in next day my 2005 Jimny dont start
2)I tried to hot wire starter and its was starting, but offten not with first start
3)I removed starter, bring it to mehanic, he opened it and there was broken magnet
4)I bought new starter, instaled it, turned a key and NO SOUND... Not a single click
5)I made hot wire on boton and starting Jimny with it. Turn ignition key on till the end, hit run boton and done
6)After a while, my check engine light came on and I feel that Im losing power
7)I attached error reader and computer was showing that engine is not runing (but it was), misfire in all 4 cilinders. Also I think my thermostat don't work, because after heavy day off-roading in muds, its was standing under half temperature

P.S.I have replaced original alternator with 160amp one, I hope its not him gilty

Finally my questions are:

a)Why my new started dont work thrue ignition key?
b)Is there relay for ignition? (Was looking in mother google and couldnt found information)
c)Can I make both key and fast start boton?

Hi

Today I noticed that my tail lights is very weak and after a few seconds fuse blowed out. I replaced fuse, again blow of... Then smoke came under streeing wheel, wires was melting. I overchecked all rear wiring and found one wire goint to mass, right next to hinges. I thought maybe now my Jimny will start with key, but nope, still not.

P.S.Can you send me photo of fuse box meaning which is under steering wheel? I dont have cover on it, so dont know which fuse is what.

My first advise for what it is worth, would be to get an auto-electrical guy sort out your obvious wiring faults before the car sets itself on fire. You do have a fire extinguisher, I hope so, you may need it. I've you-tube vids with cars going up in flames within seconds, don't take risks with fire mate...

I think safety should come first, and wiring up a fault should be very well done, Consider taking it to a good auto-electrician and only do small electrical jobs within your capabilities..

Good luck..

BGBrit.

Yea, but it was just a mistake of rear lights... That mistake was earlier too... Still dont know why my dirt baby dont start... I have seen over internet, many mentioned Suzuki Samurai kliky starter. What is that? For Samurais they just put simple relay between starter and ignition key. Could that save my day? Could it be, that from ign key is coming needed power to start up? Why there is no starter relay like other cars....

Starter relay next to battery the one without the pink wire to it

Thos little light brown ones? On one is mentioned Main, that is the one I need?