Battery issues need help figuring this out

I kind of have a complicating situation. So the easiest way to
go about this is to start at the beginning. I’ll make this as
short as possible. Boyfriend was driving my 2001 Infiniti QX4
on the freeway, notices lights start blinking and truck is
overheating. He pulls over at a convenience store. Waits a bit,
Puts water in. Tries driving again and ends up having to park
it on side of road cause he noticed the fan has completely
come off the pulley bracket. Belt is off. Blew a hole in
radiator. I have it towed home next day, get in contact with a
mobile mechanic he comes out and diagnoses it. $50. Tells
me what I need to get, so I purchase a new radiator, an
electric fan, a new bracket, and a wiring kit to engage the
electric fan. Pay the mechanic $300 to come install it all.
Does it all in about an hour. Calls me at work, tells me it all
works, everything is good. But thing is, is that my truck
battery was dead from having everything disconnected. He
never drove it afterwards or anything. I drive my truck next
day everythings fine. Next day, I get on freeway and it starts
getting hot. And rising. My neighbor takes a look at it cause
it’s no longer starting right, starts rigging shit, cutting all the
wires on the fan wiring kit, electrical taping shit, next thing I
know it’s all ghetto. After all this I take a look under the hood,
notice the battery wires are connected super bad, if barely at
all. I get new 2 way battery cable connector things for both +
and -, have to cut the cables and twist the thick gauged wires
as much as I can in order for them to fit in the metal
connector things. Then I notice that 2 wires that are striped
red and white wrapped and connected into one (which I’m
guessing are + and – which I also think are the acc wires but
I’m not too too sure,) have been exposed and the red plastic
connector has been completely taken off which was
connecting those wires to the + battery cable. So now I had
to souder those 2 wires (which were just stubs and couldn’t
be held by the cable wire connector into the cable connector)
in order for me to complete the connection to the + battery
cable. But now it seems like the whole battery issues is
worse. The jump starter I bought to jump it every time I have
to start my vehicle gets drained now and sometimes it
struggles to turn over. At times it doesn’t at all. I am waiting
for my paycheck to purchase anything I need to get cause I’ve
kind of lacked the proper things I need and I’ve put a lot of
money into this already. I don’t trust anybody else to screw
with it. If I can do this myself I will. I’m pretty knowledgeable
of vehicles. I’m not a pro or anything but I know a little more
than basic common stuff regarding vehicles and I’m usually a
good troubleshooter for a girl. Please tell me what’s wrong
and what to do!! And why I’m having such battery issues.
Another couple things to help with what you think it could be,
when I start my truck I can smell the sulfuric acid when I’m
outside and through the a/c vents. Also, when my truck is
idling or at a stop my a/c goes warm instantly and it’s only
cold when I’m actually in motion. And as of the past few days
all the dash lights and the battery light stay on while driving
and at night when I’m using my headlights they go haywire
and flicker on and off. Sometimes I have to physically go hit
the front head light for it to kick on but then the other one
goes out. Please help!! I’m about to sell this thing or start
breaking it with a hammer. I’m fed up.