I thought that his phone pinged their router on one of the other occasions (one of the 12 other times he was noted to be near 1122 King Road). I'm going entirely from memory though. I don't know his phone brand, but with both Apple and Android, if a person has enabled bluetooth while in airplane mode (say, so that their apple watch will still function or to wear earbuds), then when airplane mode is enabled the next time, bluetooth should stay on.
It's possible the phone tried to connect to a bluetooth device (which itself could have been connected to the router). Completely out of my bailiwick, but I do know that bluetooth can still work on airplane mode.
I think not. If in fact it turned out that BK was not the killer OR that there was some crazy whackadoo who wanted to claim that he or she was the real murdered, LE and DA simply do not want to give information about the path through the house. This is common to all criminal trials I've watched or been involved in. The defense will get the information, it's under lock and key, there's a reason for the gag order that goes beyond just jury selection.
With a latent print, it's common that the entire foot is not present in the print. Almost no one stomps with their foot such that a liquid would be equally distributed throughout the sole of the shoe. Often, the arch of the foot is missing in the imprint (which is valuable forensic info). If a person is running lightly (to be quiet) they will not always put their heel down (especially if they are turning). So partial prints are extremely common. A person wearing something like a knee brace may be forced to use their foot differently and give a fuller print, but you can experiment with this at home if you're so inclined (we do it in teaching labs, using washable paint from the education store).
Why would you assume both shoes were covered in blood? The fact that the print goes latent just a few meters from Xana's room tells me that not much blood was on that one shoe. I think he tried hard not to step in any blood, but because Xana was not in bed, as expected, he did anyway - but not much.
Shoe size isn't all that helpful to give out to the public. It's likely a common shoe size, from an average sized man. That does not help the public identify the person and it doesn't aid the Judge in deciding that it is Kohberger rather than someone else. It does back up what DM said, and that was the point. Indeed, since Kohberger was not yet in custody, shoe size was irrelevant - the judge needs reasons to arrest a specific individual (whose shoe size is unknown at the time).
We'll likely find out that, now that they can measure BK's foot in custody and also have his other shoes, what the shoe size was. If he were really smart, he'd have bought a special pair of shoes for his kill kit in a different size than what he usually wears (tighter would make sense, like approach shoes are supposed to be).
Wall IMO, but based on years of teaching forensic anthropology.
jmo imo