DJFuji, to your questions:
a. The input specs just tell you what the charger can accept from the wall. In USA, Canada, here we have 110 to 120 v AC at 60 Hz. In many European countries it's 220 to 240 v AC, at 50 Hz or 60 Hz. The "Hz" stands for hertz, aka cycles per second, the frequency of the alternating current. Your charger can automatically adjust for either voltage standard, and handles both common frequencies, so it can be plugged in in many places. Now, the actual plug prong configuration often is different to prevent people from making a mistake and plugging something into the wrong outlet. You can buy very simple adapters for just this purpose to allow you to plug yours into a European outlet, since it can handle the electrical characteristics properly. That is much cheaper and simpler than buying a power transformer. The "0.2 A" part just tells you the adapter will pull current at about 0.2 Amps from the wall. Other chargers that consume more probably also output a higher maximum charging current when needed. The output into the battery will be about 5 v, but you have not shown any note whether it is AC or DC. I presume there is no note about that. Some devices, like my electric shaver, have the AC-to-DC conversion system built into their own cases and are designed for a particular AC input from their chargers. Others, like battery chargers and, I suspect, your cell phone, depend on having the completly proper DC voltage supplied from the charger. The "1A" means that is the maximum current it will supply to the device. I don't recognize the "LPS" abbreviation.
b. I had to think about the term "USB Charging" for a minute, and OrooOroo provided the clue. Apparently your device is built so that it can be connected to something else via a USB cable for data exchange, etc. A normal USB connection includes two lines for DC power supplied by the "host" (e.g., a computer or a dock) to the client device. By design, these lines are limited to drawing no more than 500 mA from the host. Now many such client devices, like your cell phone, can also be hooked up to a dedicated power supply "brick" or charger instead of depending on having a computer handy to act as host. Since this charger does not have to be limited to the 500 mA that a usual host is, it would be possible to design it to provide more. However, that would be wasted if the device (your phone) were not designed to accept more power if it were available. My guess is the manufacturer would not design this way, and just stick to the 500 mA max limit. But maybe not - the dedicated charger you have is labelled "1A".
c. Charging more slowly (e.g. from a USB port limited to 500 mA max) may be better for the battery, depending on how the unit was designed. Certainly it is possible to design for much larger charging currents with the right battery and charging circuit. IF the battery is designed for faster charging at higher currents, there is little advantage to deliberately going slow at 500 mA max. However, my suspicion is that your cell phone, apparently designed for charging mainly through the USB connector power leads, may be designed for only the 500 mA max input, anyway. If that is so, and it has decent self-protection circuitry, it may never draw more than 500 mA no matter what the charger can do.
d. Is an OEM charger as good as one from the cell phone maker? Impossible to say. In each case it depends on how the overall system controls the voltage and current to the battery. IF the cell phone has all that control system built into the phone itself so that all it needs is a reliable 5v DC source that can supply up to 500 mA, either charger could be just as good because the design of the charger is not too critical. My speculation is that this is how the phone was designed, since it "normally" would function with that kind of DC supply from any old USB connector, no matter what source. BUT if the cell phone really depends on the charger to do all the regulation of charging voltage and current, an OEM device might not do quite the same job. IF you beleive them, manufacturers sometimes alert you to this by saying very prominently that you MUST use only their charger. If they don't say that, you're probably OK with OEM.
You started out by saying the 4-port USB adapter system seems to charge your cell phone battery slowly. That may be because you are using all 4 ports for something at the same time, and here's why. The car cigarette outlet supplies 12 to 14v DC, and the adapter has to cut that down to 5v DC. The cheap simple way to do that is to put inside a resistor so that, at the expected output current, about 8 volts "drops" across the resistor and thus 5v are available as output. Using 500 mA max as the output current can give you the resistor value for the design. Or it could be a slightly more complex voltage regulator circuit. But if you actually plug in several USB devices, each using, say 100 to 300 mA, the actual current flowing through the resistor is more than 500 mA and the voltage drop is greater, leaving a slightly low output voltage to the USB devices. (Even cheap voltage regulators can show an effect like this, although less pronounced than a simple resistor.) For many such devices, a supply of 4.7v instead of 5.0 would be no problem - they can tolerate some deviation from ideal. The one device that DOES have a problem with this, though, is a battery charger! If it is going to charge up a battery, it needs to give the battery a voltage only a little bit - say, 0.05 to 0.15 v - higher than the battery already is. But if the voltage available to the charging regulation circuit is less than what is needed, the charging will proceed at a VERY low amperage and be very slow. So try charging the cell phone with nothing else attached to the 4-port unit, and the cell phone turned off. See if it is much faster. IF that makes a difference, try changing your system in the car a little. You will need to "manufacture" a second cigarette lighter outlet. Maybe your car already has an extra "power outlet"; otherwise you can buy an adapter to give you two from one. Plug your 4-port adapter into one of them. Then plug the special car charger for your cell phone into the other outlet. In this way your cell phone charger will have independent access to the full cigarette lighter supply with no inteference from the 4-port adapter's innards.
Oh, you'll note I said "cell phone turned off". If the phone is turned on, whether you are calling or not, it is using power from the battery. During calls it uses more power. Even when you're not calling, if you are in a low-signal area it uses power just to keep in contact with the towers. All that power use consumes some of the charging current you are doing at the same time, so it can really lengthen the charging time. Now, I know you normally will keep the phone turned on. This is just to explain why the charging time can get longer - I'm not suggesting you stop using the phone in the car just so it will charge up quickly.
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