oh dear so many questions…
"so, which weapon do you think suitable for this build?"
whatever weapon you like the most is suitable. war scythe is easy to use, it can stunlock, it can deal fine damage and is good as a defensive weapon and good vs every other weapon (only very good players will try to parry it, others will try to flank/backstab you or attack after you missed them). uchigatana is a balanced weapon between speed, range and damage. kilij is a very aggressive weapon but has probably the best damage/second and low stamina usage. kilij stunlocks very nicely if you r1 spam. there are even more good weapons you can use in a caster/melee hybrid. but these can be upgraded as with "moon" or with "crescent". both upgrades are equal in my eyes.
"does anyone could explain how this build could overcome a pure melee type character?"
with a pure caster or a hybrid caster you can end a fight very fast and you have about the same HP as melee(str/dex/faith)-builds. actually as a pure caster you can spend some more points in vitality than for example a dex-builded character. the drawback is: you have less or almost no stamina. stamina is a main source for rolling, running, attacking etc. so its defense and offense at the same time. you compensate this matter with your high intelligence. with more spells and mana you can be very aggressive and deplete someones stamina pretty fast if you hit him. if you have a hybrid build then you will quickly change between melee attacks and spells. this gives you a tactical advantage. so yes! caster builds are very good in pvp but at the same time they are a bit harder to use in some situations.
"is shield not necessary in pvp?"
shields are awesome. i use a shield with high hit resistance to block and with a parry to set up ripostes. but shields dont fit caster and caster hybrids in my opinion, because you have lower stamina than melee builds. that means your opponent can break your guard simply by bashing you while you block them. only use a shield with a magic build if you go for pure magic melee. but then you will have only 1-2 spells and a very low manapool. still viable imo.
"also, what kind of ring and set of armors to use?"
rings as a phantom: foe's/friends ring +cling ring. rings in body form: anything you like that gives you any advantage.
"and how do you get "blessed" or "cursed" or "moonlight" thing infront of armor/weapons? I do not understand about upgrading with different kind of stone. whats the different between the 2 blacksmith that are available in the game?"
in world two you will eventually find a different blacksmith. he has the more advanced upgrades, including demon's souls upgrades. as a pure caster you want to have a crescent+5 upgrade on your weapon of choice. as a hybrid you like moon+5 more since you will have a bit more STR and DEX to make use of the parameters (you deal more damage with moon on a hybrid/melee magic build).
ok i answered all pvp related (more or less…) questions.
for the rest of the questions: please read the wiki a bit more carefully. you will find everything there.