A few questions there, some small, some big. I'll start with the small.

Our main source on whether Orwell actually killed anyone is Orwell's own account of his time in Spain, Homage to Catalonia. It's been a while since I read it cover to cover, but my recollection is that Orwell does not claim to have killed anyone, but does mention taking part in combat, including at least one close-quarters trench raid during which he used makeshift hand grenades. Not impossible that he killed or wounded someone in action then, but hardly implausible, and he likely wasn't sure himself.

His broader experience was one of frustration. Dedication to a cause, as Orwell and others found out, is no antidote to war being unpleasant business. Alongside the usual problems with military service in wartime - danger, boredom, lack of supplies, pests, weather and so on - Orwell's own frustration was built further by the army he happened to serve in. Orwell had intended to join the International Brigades - units made up of thousands of foreign volunteers (approximately 32,000 all told) who had journeyed to Spain like Orwell had. The catch was that these units were controlled by communists, in the sense that they had been organised by the Communist International (or Comintern) from Moscow, with the support of affiliated communist parties across the world. When he tried to enlist in London, the British Communist Party representative took a dislike to Orwell, and rejected him - the Party was not exactly a fan of his earlier work, and didn't trust Orwell's motives in wanting to go to Spain. Orwell journeyed to Spain independently, and ended up joining another, smaller group of foreign volunteers fighting for an organisation known as the POUM, an small anti-Stalinist revolutionary party which was connected to the British Independent Labour Party, with whom Orwell had some contacts. He fought alongside a small group of British volunteers as well as other Spanish and foreign soldiers in a POUM militia unit.

Orwell was frustrated by this exposure to the revolutionary Spanish militia system. Though Homage to Catalonia is far from uncritical of the militias in terms of military efficiency, Orwell admitted later to having sugarcoated his writing - within a few months he was fed up with the POUM and wanted to transfer to the International Brigades, which were much more traditional in their military organisation and tended to serve on more active fronts (the POUM occupied a much quieter sector). However, Spanish politics intervened - the government, supported by the communists, moved to establish central control over Barcelona, where revolutionary groups had seized key infrastructure in the immediate aftermath of the coup attempt that started the civil war. These groups resisted the government police and soldiers, leading to street fighting in Barcelona that lasted days. Orwell ended up on the POUM side of the barricades, though here at least he was very clear that he did no actual fighting and barely understood what was happening. In the aftermath, the POUM became the scapegoat for the violence and were heavily repressed, while other militia groups were disbanded and integrated into the regular army. It was this experience that shaped Orwell's writing - his anger at communist-led betrayal of the Spanish revolution outweighed his earlier frustration at the inefficiencies of serving in a revolutionary militia. You can read more about this issue here and here, and more about the militias here. If you want to read more about why so many foreigners like Orwell went to Spain in the first place, my answer here addresses this in some depth.

Your last question about the British government's perspective on the conflict (and the participation of British subjects like Orwell) is a whole other can of worms. In broad terms, Britain wanted to stay neutral in the conflict, and were more concerned with the war not forming the catalyst for a wider European conflict than who actually won. They devised the 'Non-Intervention Pact' in order to achieve this - basically, a promise from Europe's major powers that they wouldn't send arms or otherwise intervene in Spain. Hitler and Mussolini, predictably, signed the Pact and happily kept intervening anyway, sending huge amounts of direct military support to the Nationalist side for the duration. As hinted above, the Soviet Union also attempted to support the Republican side, though on a smaller scale. But from Britain's perspective, this was not the end of the world - they had the plausible deniability they needed.

That British citizens sought to go and fight, however, was unexpected and required a separate response. Britain had laws against this kind of thing - at the time, the relevant legislation was the 'Foreign Enlistment Act (1870)', which prevented British subjects from joining other countries war efforts, an Act passed at the outbreak of the Franco-Prussian War based on painful lessons learned in the American Civil War (where Britain was sued for allowing British subjects to crew a British-built ship that attacked Union shipping). The Foreign Office issued a formal notice in January 1937 that volunteering in Spain contravened this act, though privately admitted that actual prosecutions would be next to impossible, given that the UK government didn't recognise either belligerent. The formal closure of the border between France and Spain did little to halt volunteers - a route smuggling new volunteers over the Pyrenees past French border patrols (who were by most accounts not massively fussed about preventing this from happening) was soon established.

The return of the volunteers was a different matter. The British government (grudgingly) admitted responsibility for repatriating them towards the end of the war when the Republican government withdrew them from the front, including negotiating for the release of prisoners of war held by the Nationalists. Particularly on the outbreak of the Second World War, they were treated with some suspicion by British authorities, though in my own view, this was mostly directly at the volunteers who were also heavily involved in the Communist Party (which was seen as a subversive organisation) rather than a especial concern about having fought in Spain. Many ex-volunteers reported being hassled by police or employers, denied entry to the armed forces or, once enlisted, being treated with suspicion and surveilled by superior officers. The most famous case was that of Dave Springhall, who was arrested in 1943 for spying for the USSR - he received classified documents from a secretary working for the RAF, though it's hard to argue that he was arrested for having gone to Spain per se. More common was low grade suspicion and hostility, in contrast to the United States, where ex-volunteers were prosecuted during the height of the Red Scare (slightly more here).