Hi Autir,
With logical circuits, there are a number of standard specs that apply to most of the circuits. For TTL as we are dealing with here, an input senses a LOW level when the voltage is from 0 to 0.8 V, and a HIGH level when the voltage is from about 2 to 5 V. When an input is driven LOW, there is a current flowing out of the circuit of about 1.6 mA, and when the input is driven HIGH, it only draws 0.04 mA, this time the current flows into the input.
Notice that the current drawn is a lot larger when the input is LOW than when it is HIGH. A similar difference is seen with the output voltage specs: A HIGH output can source (deliver) about 0.4 mA, but sink (pull in from a load returned to Vcc, such as an input on another gate) as much as 16 mA. When sourcing a current larger than 0.4 mA, the voltage on the output may drop below the specified standard minimum HIGH output voltage, which is 2.4 V, and if we sink more than the 1.6 mA into an output, its voltage may exceed the standard maximum LOW output voltage which is 0.4 V.
Notice that the outputs can sink a lot more current when they are LOW than they can source when they are high. A number of TTL chips have "open collector" outputs, that cannot source any current at all, but they are good at sinking current. There is an NPN transistor in there, which turns on, and connects the output to ground, but when it turns off the output floats as if disconnected.
To make such outputs lines go to a HIGH level when the transistors are off, we put "pull-up resistors" between these lines and the Vcc bar, so that the resistor causes the voltage on the line to be pulled up to a level that other connected chips can understand as HIGH, above 2 V.
Now to your questions,
1. The outputs of 7446 and 7447 are designed as "open-collector", which as mentioned above, means that behind each of a segment output, there is a transistor between it and ground, that turns on and conducts current, when the corresponding segment is to light up. These transistors are somewhat heftier than the standard ones, they can sink as much as 40 mA before the voltage rises above the spec limit of 0.4 V. This means that if we pull 50 mA out, we may get 0.5 or 0.6 V on the lines, as well as a hot chip. The recommended maximum load is 40 mA.
That the outputs can sink 40 mA doesn't mean that we absolutely have to load them this hard; if we put on a load that sources 10 mA, the 7446/7447 will happily pull the output voltage down to somewhere below 0.4 V.
In the 7448, there are the same kinds of open collector transistor outputs, but here, the "internal pull-ups" are connected between the outputs and Vcc to make the outputs go HIGH instead of open-circuit when the transistors turn off. The logic of the 7448 is also inverted, the outputs are HIGH when segments are on and LOW when they are off, just the opposite of the 7446 and 7447. Like audioguru said, the purpose of this is to be able to drive other, perhaps even stronger, circuits.
2. As mentioned the 7447 pulls its outputs down when segments are turned on, and that means that the LEDs of a 7-segment display should be connected between these and a positive voltage. This may be the 5V bar, or another power source at up to 15 V for the 7447.
In addition, each of the segment LEDs must have a current-limiting resistor connected in series with it. In practice, this resistor will be between the cathode of the segment LED and the output pin of the 7447. The anodes of the segment LEDs are common connected to the high voltage, therefore the display will have to be of the common-anode configuration.
The display segments should only be forced to conduct 10 mA, and with a typical display powered from a 5V supply and where there is 1.5 V drop across the LED, and we can assume the output voltage of the 7447 to be 0V when turned on, the remaining 3.5 V has to be dropped by this resistor, and that suggest a resistor value of about 350 Ohms, where the closest standard values available are 330 Ohms or 360 Ohms. There is no need here for any enormous precision, values as high as 560 Ohms will result in a lower current and a slightly dimmer display.
You will need 7 of these resistors, one in series for each segment.
3 As we just saw, the common-anode display is used with the 7447. The CMOS 4511 is very similar in function (in fact, it has almost the same pin-out) but it drives its outputs HIGH when turning on segments, so this can be hooked up to a common-cathode display, using series resistors, much the same as the 7447.
I have no idea which one is the most commonly used; the larger displays tend to be common anode, simply because it is easier to drive them with a higher voltage (the segments may be 2 or more LEDs in series) with open-collector drivers like the 7447 or even just buffers like the 2003 or 2803. Smaller displays are common as both kinds; my experience with multiplexed ones is that the common-cathode ones are slightly easier to deal with, with a hefty 2803 or similar driving each entire digit, and the segments driven in turn by something like the 4511 ...