There are now 3 .sols that can be edited to change stats, changing Experience and Monies in SavedGame works, but affection, stats and HP appear to have checks.

If you put experience to anywhere above 30000 the game appears to glitch out, but 20000 is safe to start with and play the game through.

Secret Medals:

Become bitter enemies with Haruka.(50 pts)
Become good friends with Haruka. (50 pts)
Beat the Giant Floating Head boss. (100 pts)

EDIT:
Secret codes:
536 Rataan Way
184 Hopkins
Seaside Town -> 96 07 00 08 02 07 f4 01 00 00 -> 96 07 00 08 02 07 01 00 00 00  Makes fight easier
Castle Town

There are a couple more secret codes you forgot to mention. Each one gives a +5 weapon before you get the sword... not super helpful, but I'll list them anyway.

2015 Neil Avenue - Useless Piechart weapon
1691 Olivine Street - ShadowDeeps' Dictionary weapon
7201 Trash Street - Shuriken weapon (it's misspelled in-game as "Shruiken" unless that was deliberate)

And in case anyone doesn't know what the addresses that Master_X posted do:

536 Rataan Way - Takes you to the captain so you can get to the Island of No Return
184 Hopkins (184 Hopkins Hall also works) - A useless "burn the rope" boss with no actual fighting
Seaside Town - A boss fight with "Floating Head" that gives the last secret medal when beaten
Castle Town - A boss fight with "Marcus" that gives no items and doesn't affect the story

2015 Neil Avenue
1691 Olivine Street
7201 Trash Street

Those are the only ones that worked for me, everything else told me to find out the addresses instead of guessing.

On a separate note: Do I have to reach a certain level before I can leave this town? I've upgraded all my gear and I'm level 7 now and getting rather bored of clicking attack.

Those three you listed only work in chapter 1, the other addresses only work later in the game. You don't have to be a certain level to leave the town; just enter the address 1141 Beach Street to progress the story.