in regards to equilibrium in exchange and production.

Question

An exchange economy is characterised by the number of agents in it, the preferences or utility functions of the agents, the number of goods and the endowments of the agents.
by looking at my notes i gather that in a case where there are only two agents (a,b) and two goods (x,y) an exchange economy can be represented by an "edgeworth box". i understand that general quilibrium occurs when the market clears.

questions:
1/ what is general equilibrium and partial equilibrium?
i think partial is the short run equilibrium as at least one factor will be fixed. and genral equilibrium is the long run with all factors being variable. is this correct?

2/ how does the "edgeworth box" work?
i can see two demand curves; one for consumer A convex to "origin A" for good x and y and one on the opposite "origin B" for consumer b for good x and y. i don't understand the where the price line comes from and what is initial endowment nor the contract curve. hence how to determine at which price for each good the market will clear.

if you know any good websites that have in depth discussions please point me in the right direction. thankyou

As for number 2, Wikipedia gives a fairly good summary. Google Edgeworth box.

As for number 1, General vs Partial equilibrium is not so much a question of long run vs short run. Partial equilibrium looks for equilibrium conditions ASSUMING all other markets (or all but one other market) are fixed and in equilibrium. General equilibrium looks at interactions between markets. It looks for simultaneous equilibrium conditions in all markets. So, as one market moves towards an equilibruim condition, it is having an impact on other markets. Adjustments in othermarkets have feedback effects in the market of interest.

Again Wikipedia has a fairly good summary. Google general, partial, equilibrium

your airplace crashes in the pacific ocean. you land on a desert island with one other passenger. A box containing 100 little bags of peanuts also wash up on the island. The peanuts are the only thing to eat.
In this economy with two people, one commodity, and no production, represent the possible allocations in a diagram, and explain why every allocation is pareto efficient. Is every allocation fair?

What is difference between inferior goods and normal goods? Thank you