you may be interested in some previous discussions on this - see this post, which has links to few more

• I imagine dogfighting between two planes would create a huge ammount of stray bullets travelling a good distance. Are there recorded cases of civilians or soldiers dying because of them?

This isn't to say it never happened, far from it, but I've never encountered a single report of a casualty that was definitively from a stray bullet from dogfighting overhead.

There are however, accounts of people being killed or injured from falling shells from anti aircraft fire as well as injuries from falling shrapnel from the anti aircraft artillery shells. Indeed, so much of it would rain down, especially on well protected and heavily targeted or trafficked areas that children in England often collected the shrapnel and even traded it. Generally such shrapnel bits would be somewhat small, but could potentially be lethal if say struck on the head. As for such injuries and deaths, generally injuries were minor, as the shrapnel and falling bits would hit terminal velocity and tended to be small enough and light enough that they would not be lethal. However, occasionally anti aircraft shells would fail to detonate in the air (as they're supposed to, as they are designed to be launched into the air and explode at a predetermined time/altitude, and later with the American proximity fuze either after a set time for self destruct or when coming within close proximity of a target). Failing to detonate, and gravity being what it is, the shells would eventually fall back to earth. But they need not even detonate upon impact to kill, because they are heavy enough and streamlined enough to have a high enough terminal velocity that can easily prove to be lethal.

Now that said, I have come across a few accounts (sadly, often children) of people being killed and wounded by stray rounds/debris/shrapnel from aircraft making strafing runs against ground targets (though sometimes it's hard to tell if the account is telling us they were hit by an actual stray round or ricochet/deflection, or stray debris/shrapnel from say the target exploding, etc)

Now again, I must reiterate that just because I haven't come across a definitive account (such as a person being admitted to a hospital with a round from a German 7.92mm MG15 machine gun or a British .303 machine gun or whatnot that could have only come from a recent air battle as opposed to ground fighting) doesn't mean it hasn't happened. I would be actually be very tempted to bet my life savings that just based on odds alone, it has happened. After all, many people are struck by, and sometimes even killed by, falling bullets from celebratory gunfire each year. As for what kind of injuries to expect, be they lethal or not, that would depend on a lot of factors. Perhaps contrary to what might be expected, such incidents may often prove to not be lethal. Even a bullet fired roughly horizontally and parallel to the ground at altitude should slow to terminal velocity before hitting the ground. If fired in such a matter that it maintains the optimal aerodynamic profile, this terminal velocity could still potentially prove to be lethal however. But if the round has started to tumble, it very well could be survivable. Of course, higher caliber rounds could prove to be much more dangerous, especially cannon rounds with an explosive charge. Though some cannon rounds were fitted with timers to self detonate after a set period of time, such as some German 20mm and 30mm rounds.

Fortunately, during many air battles such as during the strategic bombing campaign over Western Europe and Germany, the Battle of Britain, etc, where you could potentially have hundreds or thousands of aircraft in the sky (each packing multiple guns and cannon, up to six or eight for fighters and upwards of a dozen or more for bombers) most people would have taken shelter that would protect them from such dangers. Even simply sitting inside your own house, while not safe from bombs, would generally be enough to protect one from the vast majority of stray rounds (except perhaps very low level combat taking place very close to your house, and of course construction materials would come into play, etc). But fighter sweeps or tactical bombing missions with smaller numbers of medium and/or light bombers and fighter bombers might not draw out the air raid sirens, and smaller villages and rural areas might have no sirens at all or bomb shelters. And even in more populated areas, in some cases, you had people gathering to watch the aerial combat unfold, such as on the coast of England people gathering to watch the dogfights over the Channel.

That said, there are absolutely accounts of collateral damage from crashing aircraft. Despite some accounts of heroic efforts by many pilots to try and steer their crippled aircraft away from populated areas, sometimes this just wasn't possible. Either the aircraft might be uncontrollable, or the area just too crowded and heavily populated. Or the pilot may not even be alive, or perhaps has exited the plane and it has continued on its own accord blissfully aware (as runaway machines so often are) that it's headed towards a house. But just as we might find accounts of pilots doing their best to protect those on the ground, there are accounts of pilots supposedly setting their plane on course to deliberately hit something after they've bailed out. I'm pretty sure I've never encountered an instance of someone claiming to have set their aircraft on track towards a civilian area before bailing out themselves, as such a claim would stand out in my mind (I have read of pilots attempting to aim their aircraft in the general direction of the enemy before bailing out though, in the slim hopes it might do some damage). I have read of a few accounts of pilots continuing to shoot at a crew-less plane after the crew had bailed out in an effort to bring the plane down earlier and somewhere safer however. This also served another purpose however, in that it could engage the gun camera and would thus record the final moments of the aircraft and confirm the kill.

I'll try dig out some instances of crashed aircraft causing collateral damage a bit later today (hopefully after I manage to get some sleep!), but most of the ones that I vaguely recall at the moment took place during the Battle of Britain. I suspect, though I'm speculating here, that perhaps a lot of such incidents went unnoticed or rather unreported when it came to some of the massive strategic bombing raids carried out by the Americans and British against Germany, simply due to the sheer destruction wrought by the bombs. A bomber crashing into a village or part of a large city that wasn't currently under attack may stand out and be noted and recorded, but a bomber shot down over, or very near the target site would just be little more than a drop in the bucket compared to the entire sections of cities leveled by the actual bombs. It could potentially go almost completely unnoticed amidst the rest of the wholesale destruction.

One incident that does stand out was actually a training exercise, which while maybe not fitting the exact criteria of yours, fits the spirit at least given that it was aerial combat training. In mid 1941, a flight of RAF Bolton Paul Defiants were on a training mission and told to make mock attack runs on a Bristol Botha aircraft also on a training run. The Botha however was unaware of the incoming mock attack, and so made some evasive maneuvers to avoid the "attacking" aircraft. Only it ended up crashing right into one of the Defiants in mid air, and a large portion of the debris from the Botha fell onto Blackpool Station, and inflicted heavy damage that resulted in the death of 12 civilians. All told, 18 died, the 12 civilians as well as 4 in the Botha and 2 in the Defiant. The Defiant actually crashed into a house, but the occupants survived whereas the crew did not.

Another incident would be that of an RAF Mosquito returning from a raid over Germany. It had taken damage during the raid, and crashed into the Bawdeswell church. The crew of two were the only casualties, but the church was destroyed. So again, not a direct result of an actual dogfight per se, but sort of in line with your question.

Anyway, like I said I'll try and dig out some specific examples, but might be awhile. Going on 11am with no sleep and I think most of the accounts I have are in actual books as opposed to eBooks, so searching might be slightly slower.