1. I don't think that there is a roll made by your character that would determine the level of the found treasure. Nevertheless, I think there exists something like treasure level in the game and that the level is fixed. The chests in Brimloch Roon are better in general than those in Valeia. Well the difference isn't big.
2. The Gold Digger trait: perhaps, the trait improves the hypothetical treasure level. Thus, the ratling has a chance to find better items. I think that the Gold Digger trait can influence only the random part of the items in the chest.
3. I think that the game uses another strategy. Many chests always contain certain items or certain class of items. The rest of the contents (if any) is random and it is chosen according to the threasure level. Examples:
- many chests contain ankhs. Let us note that it always is the same chests that contains ankhs. You cannot find an ankh in another chests. The type of the ankh can be even fixed. For example, the chest on the warrior's path in the crypt always contain ankh of STR.
- the contents of some chests is (almost) fixed. For example, the chest near Jathil at the burial grounds always contains Crusader Helm +1, 2H Great Sword +1 and Plate Mail +1. The chest may contain other items. The chest behind the "level 12" lock in the Skull Castle always contains Wizard's Robe +4, two books of magic (random spells, usually higher level), Rod of Death, and it may contain Ward of Magic. The chest with the Ash of Anephas in the Anephas Shrine contains 8 ankhs. And so on.
Therefore, it is necessary to know which chests we must open
.