It's one way to measure a workout's "work" and track progress. Tony Gentilcore discussed it, Rippetoe discusses it here with regard to the Texas Method, Dan Trink laid out a way to use it here, Dan John briefly talked about tonnage here.
Lifter A did more volume. Load is not a factor when determining volume.
Correct. The total sets and reps stayed the same, so the volume remained the same. 3x10 is the same volume as 3x10 and 10x3 and 5x6 and 1x30. Volume doesn't live in a vacuum, so load and intensity are relevant to the results of the overall program, but if you're looking at volume, you only need to know the sets and reps.
There's no numerical value (other than the optional RPE, like DT said), but for decades, intensity in bodybuilding was measured by how close the lifter gets to muscular failure on a given set. Leaving reps in the tank is lower intensity, hitting failure is higher intensity, using intensity-boosters like forced reps, rest-pause, or drop sets to train past muscular failure increases the set's intensity even further.
Depending on how many reps were left in the tank, yes. Doing 6 reps with an 8-rep max weight would be considered moderate intensity. Doing 3 reps with an 8-rep max weight would be considered low intensity.
The volume and intensity issue is why we categorize Dorian Yates' chest workouts (with 3-4 exercises, 6 total sets, and rest-pause, negatives, and forced reps) as low volume/high intensity, and Arnold's chest workouts (with 4-5 exercises, 16-20 total sets, and going "only" to muscular failure) as high volume with relatively lower intensity. We absolutely don't need to know the load they're using to know volume and intensity.
But, again, the muddy part is that when we're talking about strength-focused training (Westside, 5/3/1, etc.), intensity is measurable because that type of training generally doesn't involve muscular failure and instead requires weights at varying percentages of a rep max.