Let me start by saying that conventional wisdom is that invokers shouldn't fight at the lower levels. They should try like hell to level to at least about 40 ASAP. Many of the toughest invokers in recent memory have worked on this philosophy.

Now, I'm about to tell you that's all crap, but I wanted you to be aware that mine is something of a minority opinion before I continued.

Exploration and killing mobs first: The answer that would best serve you right now is, you can't do these things alone. You might be well served to think of your character as like the archer/artillery division in a medieval army -- not meant or able to really deal with the thick of combat (tanking, in CF terms) but able to dish out a lot of punishment/damage if others stand in the way. Group with a warrior or assassin or someone who can take the blows, and lay down damage from behind them.

PK next: an invoker is incredibly deadly at the low-midlevels. Often, you won't be able to live through three rounds of combat. That's okay, because if you play your cards right, your opponent will be dead after two. An invoker can't solo PK for long and be undefeated at those levels; it can, on the other hand, kill a lot more than it dies.

A bit of preparation can be useful here (e.g., flight for opponents likely to trip you), but honestly, it only goes so far and you can throw the whole wad at someone and still get smoked. Ideally, you just want to not tank if you can help it. Mercenaries are an option up to a point here, and PC groupmates are a much better one. Working without them, you can try to catch your prey fighting a mob or someone else and lay into them.

Good luck! An invoker is unmatched magical firepower, but it's also one of the most fragile characters in the game in many circumstances and in many ways.