Bill,
First question: It depends. Here's the Advisory Circular which applies:
http://www.faa.gov/documentLibrary/media/Advisory_Circular/AC20-30B.pdf If I'm reading that correctly, the PA-12 would not require an anti collision light to operate at night, based on the date of certification.
Also, here's the regulation pertaining to USE of lights on aircraft:
[h=2]§91.209 Aircraft lights.[/h]No person may:
(a) During the period from sunset to sunrise (or, in Alaska, during the period a prominent unlighted object cannot be seen from a distance of 3 statute miles or the sun is more than 6 degrees below the horizon)—
(1) Operate an aircraft unless it has lighted position lights;
(2) Park or move an aircraft in, or in dangerous proximity to, a night flight operations area of an airport unless the aircraft—
(i) Is clearly illuminated;
(ii) Has lighted position lights; or
(iii) is in an area that is marked by obstruction lights;
(3) Anchor an aircraft unless the aircraft—
(i) Has lighted anchor lights; or
(ii) Is in an area where anchor lights are not required on vessels; or
(b) Operate an aircraft that is equipped with an anticollision light system, unless it has lighted anticollision lights. However, the anticollision lights need not be lighted when the pilot-in-command determines that, because of operating conditions, it would be in the interest of safety to turn the lights off.
Again, you'll note there is no specific requirement to use an anti collision light, unless one is installed.
Second question: Not required. In fact, there's no requirement for ANY lighting on a daytime operated aircraft. Note, however, from the regulation above, that SUNSET is the cutoff, even though it's pretty light out for some time after sunset, POSITION lights are required for flight after sunset, in the Lower 48.
That said, I think an anti collision light is pretty important for night operations. And, with the new LED lighting systems, they don't draw any current, wiring is small, etc.
MTV