Based on my limited understanding of Norse Mythology and their views of the afterlife, Norsemen who died in battle have a 50/50 chance to go to Valhalla or Fólkvangr. However, if one died from sickness or old age, they would end up in Hel.
Would my wound earned in battle which subsequently develops a bacterial infection count as dying in battle? Would it count as dying from a sickness? Would it depend on how long after battle the wound kills me?
Also, let's say, in another example, I trip and die from splitting my head open on a rock while charging the enemy line. Would this count as a battle death or something else? Would it matter how far from the enemy I was when I died?
Who knows? Certainly not the Norse/Vikings.
There never was one single "Norse mythology" that was doctrinally consistent over the Norse/Germanic world temporally or geographically that we can look to for an answer to your question, much less all of the various possible scenarios and caveats that you also asked about. We have no written records from Norse pagans to answer such questions.
The stories that Snorri Sturluson edited and compiled into his own works almost certainly were not the same as the stories that held sway in Sweden in the 9th century, or he Danelaw in the 10th century, or Saxony before its conquest by Charlemagne. Indeed Snorri's own work was compiled centuries after conversion to Christianity in Iceland, long after remnant communities would have stayed pagan. Indeed, even the Eddas are inconsistent on who gets to go to Valhalla or Freyja's Halls, and many sources make no mention of Freyja's halls at all! So it may have been entirely a later fabrication with no actual basis in the viking age itself, the sagas, various surviving stories, and other limited literary sources that we have are at best fragmentary.
To be clear though, using these sources to try and reconstruct the cosmology, theology, eschatology, beliefs, practices, rituals, and view point of Norse pagans is a fool's errand. The sagas have about as much to do with the practice of Norse paganism as Disney's Hercules does with Graeco-Roman paganism of the 4th century BC.
So with that out of the way what do we know about Norse paganism and how it worked for someone like Snorri?
We are largely left with archaeological evidence (physical objects such as rune stones, artifacts, place name evidence, and so on), contemporary accounts from outside the Norse world, and extremely curated selections from the surviving corpus of Old Norse literature. So what do these sources tell us? What secrets can they reveal to the intrepid researchers of today?
In short, that the old Norse pagan religious tradition was elitist and extremely insular (not to mention barbaric, including human sacrifices and, if Ibn Fadlan is to be believed, the ritualized gang rape of slaves) with little popular participation and little buy in beyond the nobility. Norse paganism was hardly a core aspect of Norse "heritage" if the rapid and successful conversion to Christianity is a useful metric to go by. Indeed the religion likely varied extremely among the vast majority of the population and the paganism practiced in one part of Scandinavia likely bore little relation to that practiced in another. Evidence from across the Norse world shows that there was a great deal of variation in practices such as burial (cremation vs inhumation) and local cult popularity (as evidenced by the wide variety in theophoric place names).
The charismatic aspects of the religious tradition, veneration of Odin, ship burial/cremation, Valhalla, were probably the exclusive domain of the aristocratic elite of the Norse world. The average Norse person would not have been a participant in the same religious life as the elite of society. The average farmer, trader, slave, who lived in the Norse world almost certainly did not share the same conception of their own religious tradition as the elites of Norse society did. What good would Valhalla be to a farmer after all? Instead their worship likely focused around less well known deities with far less ostentatious displays of piety and worship.
This inconsistency in the sources and differences between social classes and across geographic spaces seems to indicate to me at least, and certainly to plenty of scholars who have fancy degrees, that there was never any sort of doctrinal coherence to Germanic paganism or Old Norse practice. So this is a roundabout way of saying that while your question is a reasonable one and certainly an interesting one, it unfortunately will likely remain an unanswerable one.