I bought the Riro carbon crank. What kind of bottom bracket do you use for this? Can you recommend anything?
The frame has a T47 86mm but the riro cranks exist in both 24mm and 30mm versions afaik. You need to figure out which one you bought and buy a T47 86mm according to the crank spindle size
I've already read here that the TanTan handlebars aren't that good, so I'd like to order a different pair. What size would you choose for the Lexon Unox?
this is entirely personal and nobody can answer that for you. you either get a bike fit or have an existing bike that is comfortable (and comparable in use, a gravel bike isn't a beach cruiser or a TT bike) and shove it in a geometry calculator to see how much reach you need for the same fit
the components you chose are all compatible from what i see, but do bear in mind a road cassette on a 1x gravel bike is going to be quite hard, unless you are very strong or live in a
boring shitho- flat place. alternatively, i'm personally not a fan of shimano rotors after using iiipro rotors