It will sound the alarm if I set it at 8:00 for example and set the alarm hand to 8. So could you set it for say 8:30 or 8:35?

You can set it to (roughly) any time you want between hours. But, of course, by the nature of the design, it won't be super accurate "down to the minute" that we take for granted with digital clocks. You are probably doing well if you get +/- 10 minutes...

A standard little neon bulb. GE made a big deal out of that plastic diffuser back in the day - interesting reading. You can replace the bulb (better do the resistor, too) easily.

As to the SUNBEAM, I've seen them. They're really poorly built. I was able to fix one for a friend who valued it as a remembrance from her grandmother's house. Took two donor clocks and a lot of JB Weld and careful Dremel work on a pawl.

Pity, there were kinda cute. But absolutely awful build quality, even for that era.