I was taught in history that people signing up together in whole towns to form a single battalion was initially encouraged, but then stopped in favour of splitting people up to prevent moral crashing at home when said battalion got wiped out by a single machine gun.
I was never told anything about what it was like to be in the town at the time (either as a visitor or as a resident). I'm talking about the British side, but I wonder too whether it happened in France, Germany, etc.
This answer I've given previously should be pertinent.
that people signing up together in whole towns to form a single battalion was initially encouraged
This was certainly encouraged, the British Pals Battalions being the units I believe you are referencing. This had to do primarily with a lack of any sort of system for creating units and distributing manpower, itself a consequence of Britain having no system of conscription. As a result, Regiments raising the forces of so-called 'Kitchener's New Army' raised Battalions locally, recruiting from the same communities, which helped to foster a Regimental pride, ethos, and unit cohesion.
The problem, of course, as you allude to, was that units that were hit particularly hard would have their losses concentrated in a few communities. Accrington in Britain, and the Dominion of Newfoundland come to mind, in the context of the First Day of the Somme.
As to your other points:
I'm talking about the British side, but I wonder too whether it happened in France, Germany, etc.
I'm less familiar with these cases, but both began the war with conscription and with professionals and reservists. There were large numbers of volunteers, but most men would have been conscripted when their turn came/if they were eligible, and volunteers would be fed through a similar manpower system. Divisions and Corps drew there forces regionally it seems, especially with distinct corps in the German Imperial Army coming from Bavaria, Saxony, Baden and Wurttemberg, but they had a wide pool of recruits.
but then stopped in favour of splitting people up to prevent moral crashing at home when said battalion got wiped out by a single machine gun.
The move towards conscription had already begun in 1915, with the establishment of the Derby Plan, which recruited through compulsion. Lists were made of eligible men that had not enlisted, and government servants and/or recruiting officers would visit these individuals, either recruiting them on the spot (with their consent) or extracting a written commitment to enlist soon. This raised c. 800 000 men; by comparison, over 150 000 enlisted voluntarily in the first week of September 1914, and over 1 million in total had enlisted voluntarily by January 1915. In January 1916 ten, Conscription was introduced for unmarried men not in protected employment (c. 500 000 soldiers were sent home from the Western Front in 1915 to work in Industry), and this was extended later that year to married men. The point here is that the heavy losses of July 1916 onwards post date the decisions for compulsion and conscription, which did away altogether with Pals Battalions.
Furthermore, just on the military side, while machine guns offered significant advantages, it was the full arsenal at the Germans disposal, artillery, rifles and machine guns that wreaked havoc, from extremely solid positions, on July 1st. Aside from the bloody initial advance by the Devonshires, which was held up by an MG that survived the otherwise thorough bombardment on the southern front of the Somme, I have yet to find examples of 'whole battalion's wiped out by a lone machine gun. That said, there was success, permanent and not, on July 1st. South of the Albert-Bapaume Road essentially, Fricourt more specifically, all British objectives were captured. North of the road, the 56th London and 36th Ulster Divisions successfully penetrated the German first line opposite them, with the Ulsters occupying the Schwaben Redoubt until nightfall. A foothold was also achieved in the Leipzig Salient, while elsewhere companies, platoons, and groups of various sizes managed to fight through, though this does little to mitigate the overall results. That also said, the majority of the divisions involved in the most successful attacks, in the south, were New Army divisions, while the majority of those in the north were Regular and Territorial Divisions of the pre-war army, though realistically the originals were thin out among the ranks. The Derby Men and Conscripts did not begin to arrive en masse until late August-September 1916; before that point, on the Somme, at Loos, and at Ypres, the overwhelming majority of British soldiers were either Professionals, Reservists, or Volunteers, doing what was expected of them or doing what they had volunteered to do: Fight.
Peter Simkins books Kitchener's Armies and From the Somme to Victory are excellent for this subject, for anyone interested.
Finally:
I was never told anything about what it was like to be in the town at the time (either as a visitor or as a resident).
From what I've read, although not specifically about those towns whose Pals Battalions were hit hard, reactions were most often shock and grief; such was to be expected in light of tragedies of that scale. However, observers in Britain and from afar, such as Australian War Correspondent Charles Bean, all seem to have been unanimous in the incredible stoicism and endurance that they saw displayed by communities. 1916 would see the film The Battle of the Somme shown before audiences across Britain and the world; it remains the most widely viewed film in British history, and reactions to it certainly represent a way of gauging public opinions. The film did little to hide the horrors of the war: dead and wounded German and British soldiers were depicted, the conditions in the trenches, explosions and artillery fire, and even staged attacks in which soldiers 'died'. Reactions to it were overwhelmingly positive, in a sense that people rallied to the cause with grim determination. Casualty lists appeared in the papers, letters arrived home from loved ones, as did dreaded telegrams informing people of a loved one killed, captured, wounded or missing. Wounded soldiers and soldiers on leave came home, and photographs and even film like that above from the front, gave British civilians a much better of what it was like and what was at stake, than they are generally given credit (either at the time, after the war, or in subsequent memory).
For the social history aspect, Trevor Wilson's Myriad Faces of War remains the best with regards to wartime Britain, though Adrian Gregory's The Last Great War and Catriona Pennell's A Kingdom United are also excellent, and more importantly, based on recent research. Janet K. Watson's Fighting Different Wars is also excellent.