What is wrong with my vehicle

I was driving down the road an came to a stop at a stop
sign an I heard this weird kind of squeak didn’t think
anything of it because my mustang never did it plus there
were vehicles that were passing me so I kept driving got
to a gas station was fine then started to drive again An my
foot was fully on the gas petal but it felt like I was playing
with it going fast then slowing down then it stopped so I
made another turn an as im almost home about two
maybe three miles from my house I started to notice that
my rpms were dropping at a very high speed an my car
came to a complete stop luckily no one was behind me
had to put it in park took the key out waited a few minutes
started it back up got it home had my mother in law take a
tester to it because when it stopped the engine light came
on plus the battery but my engine was off but all my lights
an radio were still on plus i have a brand new battery in
my car so I truest don’t think it is my battery but nothing
showed up with any codes because when I turned the car
off an turned it back on the lights went off so we took it
for a drive nothing happened so I got back home getting
ready for work an about to leave for work I had my car
idling while I get everything situated in my car An the rpms
start to drop again so I gave it a little push to the gas petal
an it became normal so I still had it in park an I called my
mother in law again An as I am on the phone with her it
stalls out again with both the engine light an the battery
light on but all my lights an everything are working but my
engine I don’t know what is causing it an I can’t check it
unless the lights come back on again please someone
help me