Bought a conversion kit, then wondered if the 1E expansions are playable under 2E rules. Anyone?

Generally, no. I think there are a few custom scenarios in place that attempt to update 1E quests into 2E, but not for everything. Except for the conversion kit, the first and second editions are very much separate games, and pretty much incompatible.

No, they aren't.

The Conversion Kit converts 1E heroes and monsters so they can be used in 2E quests. It does not do anything for 1E quests. The quest mechanics themselves are substantially different between 1E and 2E.

There are homebrew efforts to convert 1E quests to work with 2E rules, however, I would expect you will still need at least a copy of the 1E core box to make such conversions work. RtL or SoB by itself will not have enough tiles to build any of the maps, for example - they were designed to require the 1E core box at a minimum. 2E's tiles are much different from 1E's tiles in shape and layout, so I doubt you'd be able to recreate those maps using 2E tiles.

Alright, thanks for that :-)