"How was Surveyor-3's location known to such accuracy?"
The Surveyors were located using Lunar Orbiter photography (not necessarily of the probe themselves, just the surrounding area).
These coordinates were obtained by determining the position of the
landed Surveyors on Lunar Orbiter photographs by matching features
shown in Surveyor pictures ...
(This answer doesn't directly address the question, but it dovetails well with Organic Marble's on-topic answer.)
On the landing approach, Conrad saw and identified "Surveyor crater" very quickly after the "pitchover" maneuver that allowed a surface view out the windows of the LM. This was a 400-foot wide crater inside which Surveyor III ...
The Apollo 12 Preliminary Science Report contains a section on Surveyor 3.
Among other findings:
no evidence of "cold welding" of the parts.
dust kicked up during the landing of the Apollo 12 LM pitted and "sandblasted" one side of Surveyor
micrometeoroid pitting was light and confirmed the estimates used in designing the Apollo spacecraft to withstand ...
Surveyor measured the rate of descent with radar by using Doppler shift.
From the book Planetary Landers and Entry Probes:
The surveyor lander used a pulsed radar to generate an altitude reference at 100 km, a separate RADVS (Radar Altimeter and Doppler Velocity Sensor) turned on, using a four beam frequency modulated continuous wave technique (Figure 5....
To be precise, the astronaut is posing for a "tourist picture", rather than examining Surveyor.
This is photo AS12-48-7136 (very similar to -7135, but distinguishable by the position of the Réseau marks), with some contrast changes. According to the Apollo 12 image library, there was some back and forth of cameras and magazines because of a mechanical ...
It's the soil sampling arm and scoop.
This Surveyor mission was the first one that carried a surface-soil
sampling-scoop, which can be seen on its extendable arm in the
pictures. This mechanism was mounted on an electric-motor-driven arm
and was used to dig four trenches in the lunar soil. These trenches
were up to seven inches (18 centimeters) ...
Have there been any measurements on neutron radiation performed by the Surveyor (or later) missions?
The Lunar Reconnaissance Orbiter (LRO) has several instruments designed to determine the radiation environment of the moon.
The Cosmic Ray Telescope for the Effects of Radiation (CRaTER) was specifically designed to "...characterize the lunar radiation ...
No, the propellants have changed from bipropellant to solid or monopropellant.
I can't confirm the exact engines of Surveyor and Viking, and I'll take your word that they were TD-339. Viking used bipropellant.
Pathfinder/Sojourner use solid rocket engines.
MSL(Curiosity) used monopropellant.
MER(Spirit and Opportunity) used monopropellant.
InSight used ...
The Lunar coordinates of the landing site were 3.01239° S latitude, 23.42157° W longitude which Ewen Adair Whitaker ( who had previously successfully located Surveyor 1 for NASA) designated as 1,180 feet (360 m) from the location of Surveyor 3, a distance that was chosen to eliminate the possibility of lunar dust being kicked up by Intrepid's descent engine ...