Do the procs of PvP Items trigger in PVE

Bound items are a feature implemented in MMORPGs to avoid abuse of twinking.

Bound items are designed to prevent them from being shared with other characters, to avoid easily making overpowered lower level characters. If you have a bound item, it can (generally) be sold to in-game vendors, but it cannot be traded to another player.

Unbound items, however, can be freely traded from player to player, and can be used by players who aren't the ones who initially obtained the item (whether from quest, random drop, or by purchasing it from a vendor), assuming that the player meets all of the other requirements for the item.

Bound and unbound is not random. Quest items are typically bound, as they are the reward for that character completing the quest, and therefore it is expected that that character will be the one to use it. The same applies for specific reward drops from difficult encounters, such as raid or group instances.

From swtorstrategyguide.net's "Server Types" article:

• PvP servers are ideal for players who want to battle the other faction.
• PvE servers are ideal for players who want to play cooperative games with their own faction.
• RP servers are for people who prefer to act in character. There are usually only a few RP servers all together in an MMORPG, so if you do not know what role-playing is, this is likely not for you.

And my addition:

• RP-PvP servers combine the two.

No, you do not lose any items when killed.

There is a feature called item damage, but you shouldn't have to worry about it — in regards to PvP anyway. Let me explain: Usually if you die a lot, your character's equipped armor/items need repaired from time to time to keep functioning. Most vendors let your repair damaged equipment for the price of a few credits; the higher level the equipment the more credits. But PvP deaths do not affect this in SWTOR.

The only real issue you have with PvP servers is having to stay vigilant when questing in contested (non-faction specific) zones (level 20+ areas usually) so that you aren't killed over and over while trying to do other things. But if you have help, like your guild for instance, you can call in your friends as backup if someone is griefing you.

There should be no monetary cost to your character on a PvP server. In the worst case, only your time respawning or running back to where you were when you were killed. And even then, SWTOR let's you respawn exactly where you die, though there is a timer on that feature.