As I found in the official forums the world- and playerfiles are located in
/data/data/com.and.games505.Terraria/files/ and you need root, to gain access to this directory.
For now I found no other way to get to your savegames.
As of version 1.4: Yes, using the Luck mechanic.
Material drops and unique item drops, among a number of other things, are affected by the player's Luck, though this mostly seems to apply only to non-Boss enemies. A positive Luck score can as much as double item drop rates, while a negative Luck score can almost halve them (though in practice, it's impossible to go lower than 9/10ths the usual drop rate). Luck is affected by a wide variety of factors, most of which aren't communicated in the game.
Ladybugs and Town NPCs - Touching a ladybug that was released by a player gives a bonus, while killing a ladybug (including using one as fishing bait) gives a penalty. Killing Town NPCs affects the same variable, with the Guide giving a bonus and any other Town NPC besides the Clothier giving a penalty. Only the most recent event is used.
Torches - Certain types of Torches in the area (within about 42 tiles?) will affect a player's Luck. Generally speaking, biome-themed torches will give a bonus when in the correct biome, and Bone Torches will give a lesser bonus in non-biomed (i.e. Forest) areas. Most other torches don't affect Luck, and multiples of the same type of Torch don't stack.
- Prior to version 1.4.0.3, using a biome torch in the "wrong" biome, or using regular torches in most non-Forest biomes, would result in a penalty to Luck. This effect was removed in the 1.4.0.3 hotfix.
Luck Potions - Having the Lucky buff from a Luck Potion will increase your Luck score. Longer remaining durations on the buff provide a stronger increase.
Lantern Nights - The Lantern Night event occurs the evening after a boss or invasion is defeated for the first time, and provides an increase to the player's Luck score through the night, even underground.
Garden Gnomes - If a Gnome enemy is exposed to sunlight, it turns into a Garden Gnome, which is a piece of furniture that gives a Luck increase to players nearby (about the same range as Banners and Campfires).
These different factors all stack additively with each other.
In addition to this new Luck mechanic, the previous options for getting an item to drop sooner -- Expert Mode and increasing spawn rates -- still apply (see below).
Source: https://terraria.gamepedia.com/Luck
Prior to version 1.4: No, there is no way to increase the drop rate of items.
(With one exception for some items. See below.)
But what you can do is increase the enemy spawn rate.
Obviously, the faster enemies spawn, the more you can kill, so the more chances they have to drop the item you're after. The spawn rate of enemies can be increased in a few ways:
- Battle Potions - Increase enemy spawn rate while active.
- Water Candles - Placing one of these will increase the spawn rate in the nearby area, indicated by the presence of the Water Candle debuff active on your character. Holding one will also work, but then you can't equip a weapon.
- Blood Moon - During a Blood Moon, the enemy spawn rate in surface areas will increase.
These effects do all stack with each other, but you can't stack multiple of the same item. So the highest spawn rate increase possible is by using a Battle Potion with a Water Candle placed nearby (during a Blood Moon, if applicable).
This is the only thing you can do to increase your chances of finding an item.
But what was that about an exception?
The only exception to this general rule is Expert Mode, which is only available in the Desktop, Console (PS4/Xbox One/Switch), and Mobile (iOS, Android) versions of the game. In an Expert Mode world, some rare enemy drops will have their drop chance increased, sometimes as much as doubling. Obviously, you need to create an Expert Mode world if you're not already using one, and Expert Mode comes with its own set of complications, so try it at your own risk. If you want to find whether your particular item has an increased drop rate in Expert Mode (and what the new drop rate is), look up the monster that drops it on the Terraria Wiki.
Best Answer
It appears that blocks actuated into the background do in fact still count for a biome.
I did not find any information on the wiki that would point to this conclusion, so I decided to test it myself. I built a small area of 80 mud blocks and grew Jungle Grass on them (80 is the number of blocks of Jungle Grass required for the area to be counted as a Jungle biome, see here). I then actuated all those blocks.
Now, how do we test that this area is in fact a Jungle biome? Well, apart from the music changing (which it did), we can use the Witch Doctor NPC. When the Witch Doctor is in a Jungle biome, he sells additional items that are only sold under that condition. So I built a house for him inside the area of Jungle Grass blocks.
As seen in the image, the Witch Doctor is indeed selling the additional items (Tiki Totem and Hercules Beetle at the moment). This proves that this artificial Jungle biome is working.
Now all that needs to be done is to actuate all the blocks into the background and see if the Witch Doctor is still selling those additional items.
With all the Jungle Grass blocks actuated off into the background, the music still stays as the Jungle music, and the Witch Doctor is still selling the additional items. There are no other foreground Jungle Grass blocks on the screen, so the only explanation is that the background blocks still count towards a biome's existence requirements. Note that I only tested this with the Jungle, but it is likely that the result I found here will also apply to other biomes.