Can NM-B go inside conduit outdoors?

No. NEC 334.12(B)(4) prohibits NM cable in wet or damp locations, and the interior of a raceway on an exterior surface or underground is a wet location per Article 100.

Is THHN allowed in an outdoor conduit?

Only if it is dual rated THWN-2 or another wet rated type. NEC 300.9 makes the interior of a raceway in a wet location a wet location, which requires conductor insulation listed for wet use.

What ampacity do I use for UF-B cable?

NEC 340.80 limits Type UF ampacity to the 60 degrees C column of Table 310.16, so 12 AWG is 20 amperes and 10 AWG is 30 amperes.

Can I stub NM-B to an outdoor box and switch to UF-B or THWN-2 in conduit?

Yes, and it is the standard way to do it. The rule you have to respect is that Type NM cable is not permitted in wet or damp locations. Section 334.12(B)(4) prohibits NM in wet or damp locations, and Article 100 defines the interior of a raceway installed underground or in an exterior wall as a wet location. So the NM has to stop while it is still inside a dry space, and the transition has to be made in an enclosure suitable for the location.

Where the transition box goes

The cleanest arrangement is a box mounted on the interior side of the wall, in the dry, with the NM landing there and a raceway leaving the box through the wall to the outside. That keeps the NM entirely in a dry location and puts the wet location conductors in the raceway.

If the transition box must be on the outside wall, it has to be listed for a wet location and the NM cannot enter it, because the interior of an exterior box in a wet location is a wet location. In practice that means running a short raceway through the wall from an interior box, or bringing the NM into an interior box and pulling wet rated conductors from there.

Which conductors go in the raceway

Section 300.5(B) states that the interior of enclosures or raceways installed underground is a wet location, and 300.9 says the same for raceways in wet locations above grade. Conductors in that raceway need a W in the insulation designation. THWN-2 qualifies and is rated 90 degrees C wet and dry, which is why it is the default choice. XHHW-2 also qualifies. Plain THHN does not, although virtually all building wire sold in the United States is dual rated THHN/THWN-2, so read the print on the jacket rather than assuming.

Type UF-B is permitted for direct burial per 340.10 and is listed for wet locations, so you can also transition from NM to UF at the interior box and run the UF out through a sleeve or directly underground. Note 340.80: the ampacity of UF cable is limited to the 60 degrees C column of Table 310.16 regardless of conductor insulation, so 12 AWG UF is 20 amperes and 10 AWG UF is 30 amperes. That matters on longer runs where you were counting on 75 degrees C values.

The fittings and the sleeve

Section 314.15 requires boxes and fittings installed in wet locations to be listed for use in wet locations and to prevent moisture from entering or accumulating inside. Use raintight compression fittings, not set screw connectors, on the exterior side. Section 225.22 requires raceways on exterior surfaces of buildings to be raintight and arranged to drain.

Where the raceway passes through the wall, seal the penetration. Section 300.7(A) requires a raceway that passes from an area at one temperature into an area at a significantly different temperature to be sealed with an approved material to prevent circulation of warm air to a colder section. A duct seal plug at the box end handles it.

Field takeaway

Land the NM in a box on the dry interior side, transition to THWN-2 in raceway or to UF-B, use wet location listed boxes and raintight fittings on the exterior, and derate UF from the 60 degrees C column. Never let NM enter a raceway that leaves the building envelope.