You need to use wiring methods compatible with the wire. For instance XHHW wires aren't allowed outside conduit, so you either extend the conduit the full run, or transition to a type of cable that is rated for direct use. They do make individual wires rated for direct use, check with your supplier (who I hope isn't a big-box store).
You cannot splice in an LB. * Put that right out of your head. You'd need an appropriately sized junction box, and since we're dealing with large size wire, you need to follow the wire-radius rules, not just the cubic-inch rules. So you'd want a gutter, specifically.
1/0 may be larger than you need. 1 AWG Al should be legal for 100A (you are allowed to work out of the 75C column for >=100A feeders) and your distance isn't enough to warrant a voltage bump (put your distance, 40A for the charger, 240V and 6% into the voltage drop calc and see what it says).
The feeder run must be protected. The main breaker in the subpanel is in the wrong place to do that, so you need a 100A breaker in the main panel A normal breaker is fine.
The subpanel doesn't need a main breaker. However since it is an outbuilding, it needs a shutoff switch. Using a panel with a main breaker is an overkill, but cheap, way to do that.
When used as a shutoff switch, as in here, the size of the subpanel's main breaker does not matter. If you're getting a small-ish panel to obtain a panel with a 100A main breaker, don't do that! Spaces are rather valuable (super cheap to add now, super expensive to add later) and you don't want to have to have a future project compromised because you refused to spend a few latte's on a bigger panel today.
Also you want to avoid the necessity to go to "double-stuff" (twin, duplex) breakers simply to achieve needed density; most breakers today need AFCI,GFCI or both and that is they don't make those in double-stuff.
You need 1 ground rod if proper testing proves it to be <25 ohm to earth (this is specialized testing, not a pocket VOM) - otherwise you need two.
* Ever buy a product with 10 warning labels because some people need disclaimers to not eat things they shouldn't? Well, here's one. If the LB is excessively large for the wires that are in it, e.g. if you used a 6" LB, then you get to treat it under the junction-box/gutter rules, and count the dimensions to determine whether a splice here is legal. But normal people don't do that, because it's an expensive way to get a junction box.