Take a look at the Wiki on the page Mystic Forge. It will tell you where the forge is, how it is used, and some predictable recipes. The forge lets you do two things. First you can create recipes to craft other items like consumables, weapons, or armor. Second, the forge can be used to create better crafting materials of one type higher.
The examples the wiki gives are as follows:
Common Crafting Material Promotion
Common crafting materials can be promoted to a small pile of higher
tier materials with the following formula. The tier of dust needed is equivalent to the tier of the wanted product. So, if you are hoping to create Orichalcum, a tier 6 common material, you need to use Crystalline Dust, a tier 6 dust. If common crafting material B is one tier higher than common crafting material A, then:
10-50 Crafting Material B = 250 Common Crafting Material A (i.e. 250 Mithril Ores) + 1 Common Crafting Material B (i.e. 1 Orichalcum Ores) + 2-5 Dust A (i.e. 5 Pile of Crystalline Dust) + 5 Philosopher's stone
In that example: That recipe will produce 10-50 Orichalcum Ores
Armor boxes and armor satchels
Recipes can be created using the Mystic Forge. They will allow you to
craft armor boxes and armor satchels, which will in turn give you
every piece of an armor set.
Armor set recipe
Ingredients
5 Bottle of Elonian Wine
20 Arcane Crystal
50 Mystic Coin
1 Armor item
Mystic coins seem to be a common item needed for Food Trays, Weapons and Armor. Also look at this page for current recipe research.
You can see this in action with this video on how to make a Giant Chocolate Cake. Details are in the video summary.
It does not appear to currently be possible.
The only solution is to simply tame another aquatic or amphibious pet, thus allowing you to rotate the pets to the desired formation.
Best Answer
No, the chest will not be lost when you log out. I have left an unopened chest on the screen and it was still there the next day when I logged back on.
It is not possible to open the chest with another character, however, as only the character who completed the daily achievement will be able to see it.