The reason for the two pins connected together and to the adjuster of your variable capacitor is to ground the adjuster - those two pins should be the ground connections - this prevent the tool you are using to turn the vanes affecting the capacitance.
Also foil wound fixed capacitors often have a line around one end which signifies which lead is connected to the very outside bit of foil so that you can join this end to ground so as to act as a screen around the inside foil.
If you want to make your radio louder (but not more sensitive!) you can increase the audio gain a bit. You'll need a 1.2kohm resistor and a 10uF electrolytic capacitor, join them in series and the join them from pin1 to pin 8 of the LM386. More info here...
https://www.ti.com/lit/ds/symlink/lm386.pdf
Well done in getting your project to work - you can proud of it! I remember the very first transistor radio I built back in the 1950's - a three transistor reflexed broadcast band kitset radio in a smart plastic case - that radio went with me everywhere! Other kids of my age thought I was a genius!
You said "That's why I preferred not to go with a kit as they are costlier than building from scratch." Sometimes this is not true if the kit maker puts together a lot of kits - bulk buying makes things cheaper and you may get a printed circuit board or a cabinet to put it in for a cheaper price than you can but the individual components.