calculate voltage resistance
Thats a lot of questions in one message!
The input pins of a chip are designed to place a little load as possible on the circuit that drives them. This is so the they have least possible influence on the driver which could also be feeding other devices. The drawback to this is that because the input draws such little current, it cannot discharge a voltage unintentionally present on it. For example, static build-up or just signals picked up when the pin or connections to it acts like a radio antenna. For that reason we use either pull-up or pull-down resistors, they are a source of current to pull the pin to a known high or low voltage. The value is chosen to be low enough to discharge unwanted voltages but not so low that the circuit takes too much extra driving. Some of the drive current inevitably goes down the resistor and this to some degree reduces the amount reaching the IC itself. Sometimes the resistors (or an equivalent weak current source) is built in to the IC, sometimes you have to provide it outside.
The output pins of a chip have a circuit behind them that intentionally provides signal to drive other devices. Because it can source current from the supply when high, or sink it to ground when low, there is always a discharge path for unwanted signals so pull-up and pull-down resistors are not normally needed, the chip itself provides the discharge path.
There are two exceptions to the output pin rule;
1. Tri-state pins have a third condition, the pin can be internally disconnected from the driver behind it. This is usually to allow several output to be joined together with only one being active at a time. In a tri-state condition, the pin doesn't source or sink current so a pull-up or pull-down may be advisable. It depends on the chance of all the connected pins being tri-state at once. If any is driving, it discharges the whole network and resistors are not needed.
2. Some devices are called "open xxxx" where you can substitute 'collector', 'emitter', 'source' or 'drain' for xxx, depending on the kind of device. These can either sink current to ground or supply current from the power rail but not both. Whichever way they pull, sometimes a resistor is needed to return them to the other state.
You should not normally use LEDs connected to an IC without resistors in series with them. LEDS try to draw as much current as you let them and the resistor is needed to keep it within safe limits for the LED and the pin driving it.
Your math for the LED is correct to a point but LEDs and most other semiconductor materials do not have a linear voltage to current ratio. Their resistance will appear to change as the current changes so you can't always say it equals 244 ohms.
The correct way to calculate the series resistor is:
(supply voltage - LED voltage) / LED current
Which is what you actually did. Get the LED voltage and current requirements from the manufacturers data sheet.
Brian.