Hello, welcome to the forum, and congrats on your purchase! I'm glad that you like your car so much. Here's some thoughts on your questions:
#1: An easy way to check this would be to check what voltage your battery is sitting at when the car is turned off, versus when the car is turned on. If the battery voltage is good when off, but does not increase when on, then the problem is the alternator or the voltage regulator. If the battery tests bad, then, there's your problem!
#2: you may be missing a throttle return spring. If there is no spring to get your throttle to come back to 0, then it'll just stay there sometimes. Looks like this:
They sell them at basic auto parts stores, they aren't specific to the car - just make sure you get one that's short enough that it has some tension on the throttle rod when installed.
#3: If the fuel sending unit is aftermarket, there's a good chance that it has never read correctly. Sometimes you need to bend the arm to make sure that it is really touching the bottom of the tank (or close to it) at the bottom of its travel. You should also check the resistivity output, which should be 10 ohms at full and 73 ohms at empty IIRC (might have that backwards, but you'll see). If it's not putting out the right resistivity, then the gauge will not read right.
#4: Agree that fixing the charging system will help this issue, but the stock lights are just very dim. You can try taking the instrument cluster out and cleaning out the little plastic housing that covers the light that gives it its color -sometimes these just get full of dust so they mute the light a lot. But LEDs are a better conversion by far. Many Mustang parts warehouses sell the conversions, but I'm not sure what would be best for you in Bahrain.
#5: Power brakes will not stop you any faster than manual brakes - they only make the pedal easier to push. What power brake conversion did you use? Do you have disc brakes? What master cylinder are you using? Likely you have some mismatched parts in there and that is causing your poor stopping power.
#6: The hazard lights kit is always a good thing to install. You should also install LED taillights while you're at it, as the original taillights consist of a single dim bulb that is extremely difficult to see by today's standards.
#7: Is it a gas smell, or an exhaust smell? If the smell is raw gas, then likely some of your rubber lines are either leaking or have become porous. This happens when they get old or when someone uses non-ethanol fuel rated lines. Swap em out and the gas smell should go away. Now, if the car smells like exhaust... well, that's a bit of a tuning issue, and also a bit just how the car will smell after being driven.
#8: I've got EFI in my car. It is absolutely worth it for me, but my car is a daily driver that goes over a ton of elevation change in road trips. It will not improve your fuel mileage versus a carburetor. It will, however, handle large elevation changes much better, and will not require tuning like a carb after the initial tune is set. Additionally, it is easier to start, though that is primarily a function of using an electric fuel pump. If you've got a lot of extra cash sitting around and you want that kind of convenience, then go for it! Otherwise, leave it be.
Hope that helps!