Look into Pocket Chess Deluxe from Handmark. It is HORRIBLE to play against (Always opens up with Nf6/ Nc6 or vice versa) BUT has an excellent PGN reader. It recognizes comments and variations, and has a desktop tool you can use to load your own, or any other games in PGN format. It has 'problems' you can use to train, although it is a limited number, you need to load a few for variety. I like to use it to review games, I loaded a bunch of annotated games on to it and played through them at night.
Very interesting! A nice PGN-tool would be interesting. It would be nice to edit PGN files on the PALM (without too much fuss). There used to be a ChessPad version for the PALM but I cannot find it anymore.
If I remeber correctly they charged a few USD for the PALM version but the PC version is free.