cannot drive anything directly because the load on the R/2R ladder will change the output voltage. You will need to add some form of amplifier

drive a LED directly

A series of digital pulses where the on and off times are adjusted to deliver a required amount of energy as required

A series of digital pulses where the on and off times are equal

to move them  4 at a time

to move them all at one time

move them one at a time as they draw large currents when moving and small currents when stationary

where the excess heat in your power supply circuit is released via the heat sink

where the excess heat in your power supply circuit is shared via a resistor or series of diodes

Sharpen a knife

To electrically isolate two components 

Buy a ttl converter ic

You don't, 5V and 3V are basically the same.

Using a suitable voltage divider

Using a buck converter

To represent a decimal number by using 4 bits

To program an IC chip.

To flash a LED.

Sense for a switch closure and then go for a delay and then come back and see if the switch is still pushed

Sense for a switch closure and then read the switch instantly

Can't be solved

It is where the mechanical contacts bounce together and produce a series of pulses

It is when the switch is dropped and it bounces off the ground

Use analogue filter.

0-5V

The supply voltage range.

unknown output.

Any voltage.