Anyone kind enough to tell me the difference between pvp and pve server?And yeah, can we kill each other when we are on pve server?

Yes both can do Horde Vs Relliance fight. But in a PvE server, the opposing faction can only attack you if you're flagged. You can choose to be flagged by typing /pvp, you get flagged if you attack an NPC of the opposing faction, you get flagged if you attacked a flagged player from the opposing faction, you get flagged automatically when you're in the opposing faction's cities, and you get flagged automatically when you're in the battlegrounds.

In a PvP server, you are flagged whenever you enter the opposing faction's territories or in a contested (neutral) zone. Hence, you can be ganked while questing in a contested zone and attacking mobs while in the enemies territories are not recommended (unless you're like 20 levels above them).

Also, you can create both Relliance and Horde characters in a PvE server but you can only create characters from one of the faction in a PvP server.

Mad/Seen any suggestion what character should i build?