Borderlands – the drop chance of the Hornet from Knuckle Dragger

In playthrough 1, outside of the DLC, there's no such thing as scaling. Enemy levels are determined solely by the area they're in and your mission (certain missions effectively "level up" areas, notably Sanctuary and The Dust). You can easily check the level of an area by checking out the vending machines in the area, they sell items scaled to the level.

DLC in playthrough 1 scales to your level...ish. It maxes out at level 30. I played the DLC as a level 34 character and was disappointed to see everything was at level 30 in playthrough 1. Not sure if it has a minimum level it scales to.

Playthrough 2 works the same way until you beat the Final Boss; then everything in that playthrough scales to your level (except mission rewards for missions picked up before the final boss).

Playthrough 3 works the same was as Playthrough 2 after the final boss: Everything scales to your level, period. In team play, it will always be scaled to the highest level player's level. And you have to be at least level 50 to unlock it, so enemies are effectively level 50-61 at all times. Though if you take a mission before leveling up, the mission will still stay at that lower level, as always.

Basically the game works like a standard RPG without level scaling until you A) beat the game twice (because you should be maxed out anyway) or B) enter a DLC (because you can do that at any time so a preset level would be a really bad idea)

Vault Hunter's Relic

It has a very minor effect on legendary drop rates, that you're probably better off using another relic. It only affects white (common) and non-white drop rates (and not legendary drop rates, specifically).

From this somethingawful.com forum post by user, gibbed:

So I just investigated the Vault Hunter Relic data.

It modifies two attributes:

GD_Balance.Weighting.GearDrops_RareWeightModifier: +0.05 GD_Balance.Weighting.GearDrops_CommonWeightModifier: -0.06

Let's set them to +100.00 and -100.00!

Net result: I have not seen a single white weapon drop, greens drop, seen a few blues. Nothing else.

So, what I can gauge from this, is that it shifts a 5% of your chance for whites into non-whites. Doesn't touch anything else. Very low impact, perhaps bordering on useless.

True Vault Hunter Mode

Some of differences in True Vault Hunter Mode as opposed to Normal mode are:
...

• Better Loot: Due to the nature of difficulty increase and the fact the game becomes more difficult, in True Vault Hunter Mode there is a higher chance of enemies dropping better loot and chest also will contain better loot.
• Better Loot more frequently: Enemies in True Vault Hunter Mode will be have a higher percentage chance of dropping better loot as they have more health and are more difficult to defeat.

^{Source: Borderlands wiki, "True Vault Hunter Mode" article}