Your success rate increases as your thief's (Therion's) level increases.
There are also, in some towns, people that, if you scrutinize (with Cyrus) or inquire (with Alfyn) will give you an increased success rate. More specifically, when you do either of those actions you'll see "Thieving Tips & Tricks" in the "Information Gleaned" section of the dialog ...
The in-game tutorial states that holding down the B button will make your character dash, and increase the encounter rate as well.
Many fans have tried to work out how it exactly works, but it seems the common consensus is that it does indeed increase the encounter rate somewhat. The red minimap is indicative of the increased danger.
Rogue Path Actions have a chance of failing and can also damage your reputation if you keep failing. If your reputation takes too much of a dip, NPCs will no longer react to your Path Actions, and you’ll need to head to the local tavern keeper and hand over some Leaves (money) to bump that reputation back up. Sauce.
Noble actions, on the other hand, have no ...
From what I know Octopath Traveler is single player only.
There are no multiplayer options on the title screen. While I'm still working my way though the first chapter of each character's story, I haven't seen anything in-game to indicate there is multiplayer either.
Here is the picture of all the base class shrines + the 4 advanced ones:
The job of each shrine corresponds with the starting city of the same "biome" type i.e: scholar -> city: Atlasdam, biome: flatlands, shrine: Western Noblecourt flats.
In the example above, it would be [Atlasdam]-> North Atlasdam Flats -> Western Noblecourt Flats -> [Shrine of the Sage]...
Every time a new character joins your party, you get to play through their initial "tutorial", The Prologue, followed by their Chapter 1 story. As you progress through the game, you can play through each character's story equally.
There is no difference between choosing a certain character as your initial character, or in the order of having new characters ...
Though they both grant the same information the key difference is that using scrutinize allows you to access some information at lower levels than inquire would. Inquire requires you to be at a certain level to work, but it is a guaranteed successes, where scrutinize can be attempted at a lower level, but risking the reputation hit that a failure incurs.
There is an interactive map available at http://www.octopathtravelmap.com/ which lists the danger levels of areas.
In case the link goes stale, the general rule of thumb is that the danger level increases the further you are from the center of the map.
No, there are no other uses for these items. Without writing up an exhaustive list for each item, there is no way to be absolutely sure - but it is safe to say that each of these items are in the game for the sole purpose of selling for currency.
This is a common concept in many other RPGs, as well. For example, the Gold Nugget in Pokémon games.