These questions really aren't defined well enough to answer. In most of them I think I know the answer you are after, but the (lack of) wording makes it difficult to be sure.
1) When the number "B10101010", or "0xaa" is shifted out LSBFIRST to a 74HC595 8-bit shift register, pin Q7's state is:
a) LOW (connected to GND)
b) completely unconnected
What is "shifted out." Does this imply that SRCLK and and RCLK remain unchanged? "Shifting out" a data pattern from one device isn't the same as "shifting in" a pattern from another. For example, if clock was never toggled and only SER (Pin 14) was toggled, then Q7 remains unchanged.
2) What is the state of pin Q7' of the 74HC595 when the same number is shifted out?
Again, depends on how the clocks are being used and definition of "shifted out". Assuming the clocks were not toggled, I would expect Q'7/Q'H (aka serial out, depending on the manufacturer of the chip) to remain unchanged.
3) True or false: you can access the characters of a String by treating it as an array like this: String a = "lol"; char b = a; in Arduino.
4) Can you print this to the Serial Monitor: 鐵路華工紀念碑 ?
5) What is the ASCII number of this character: 鐵
There isn't one, it isn't an ASCII Character. It is Unicode.
6) How does pin Q7' relate to pin Q7?
Pin Q7' of What?
7) Name the short lead of an LED.
8) Name the long lead of an LED.
What about surface mount LEDs? Perhaps you meant Negative (Cathode) and Positive (Anode) sides of a through-hole LED?
9) Direct current flows from:
a) From ground up to V+
b) From V+ to ground
c) Any way it wants[/quote]
Based on Conventional or Electron Flow?