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@Necroes when it comes to movement, there are detailed rules for climbing, rappelling, jumping, swimming, diving (which is separated from swimming), treading water, and more. But no rules for crawling.
@Necroes Unfortunately, it seems more like an oversight that they left it out. Movement in the system is not abstract, it is very "crunchy" like pretty much everything else in SR5. Your movement is calculated based on your Metatype and Agility, that movement is shared across the entire Combat Turn (potentially multiple Initiative passes), and movement is broken up into walk/run/sprint with detailed rules for all three. At least when I ran SR5 a few years ago, I personally felt the need to houserule it in
In short: "Please filter game rules through common sense when 'weird cases' come up." Ex: I believe it was in 3E where the 'Prone' condition specified that you "Fell to the ground" which, if taken entirely at face value, would mean that a swimming character would either teleport to the nearest shore, or teleport to the bottom of the body of water they were in, depending on what the DM decided 'ground' was.
Alternately, just hit up the forgotten realms Wiki (or grayhawk, or wherever your character hails from) and search on domains...and just wave your hands and ignore the fact that your deity is now in a different dimension and should have no ability to project power into Hyrule.
If you're playing a game in Hyrule, there is no official D&D answer to give you. I would suggest going and hitting up the Legend of Zelda Wiki and searching for Hylian deities. And then if there's anyone 'running' the play-by-post, or moderating it, or whatever...check with them to see if one would be appropriate. But, in short, Hyrule doesn't have "Domain-specific" deities because Hyrule isn't a D&D-compliant setting. Your best bet will probably be to hit the wiki, find a deity or 'guardian deity' that looks close enough, and go for it.
To your first point--this is contradicted by the FR Campaign Setting book from 3E: "Everyone in Faerun knows that those who die without having a patron deity to send a servant to collect them from the Fugue Plane at their death spend eternity writhing in the Wall of the Faithless or disappear into the hells of the devils or the infernos of the demons." With as real and relatively unrestricted as the gods are--if they really want to make sure everyone knows the rules, they can. This statement could be interpreted as hyperbole--but, y'know, that's what it says.
@Trish Wasn't sure if it was needed, as it's essentially a repeat of what was in the 3e Campaign setting...but I added the quote for completeness sake.