To try and answer your questions...
1) There's nothing official about using the Doom track, as far as I know, but I once tried a solo game with modified doom track rules, as follows:
I decided to use modified Doom Track rules as follows:
3 discarded cards per Doom Counter
4 experience points per upgrade
Once the Doom Track was completed, if my hero did not have a set of maps AND enough gold to hire the first available captain, then they had failed. Otherwise my hero would travel immediately to the Isle of Dread and face the challenges there.
2) You must reveal a card. In the case of sea travel, something encounters you, instead of you choosing to encounter something.
3) As far as I remember the challenge is discarded. I think this only happens if you successfully flee, otherwise you've either won or died.