I'd try a light missile caracal in level 2 missions, if I remember correctly there are mostly smaller enemies in those missions that you'll hit better with smaller weapons. You'll be slower to kill the big ships, but a lot faster for all the small stuff.
You should also change your tank, usually you'd use something like two large shield extenders and 1-2 Adaptive Invulnerability fields, all depending on your fitting skills of course. Small shield extenders are a waste of a slot, you'll always want to oversize them: Medium Shield extender on frigates, large ones on anything bigger.
Warrior drones are the fastest ones, you might want to train Drones to V, so that you can learn Drone interfacing (+20% per level). That makes a huge difference for your drone damage, and you'll need it for the higher level missions in any case.
The Target Navigation Prediction skill also helps with hitting the small ships with missiles, and also the more expensive Guided Missile Precision skill.
Here's an example fit for a missioning Caracal, you can of course downgrade all the T2 modules if you don't have the skills to use them. You can also change the invuls to rat-specific hardeners, that should further improve your tank. Though that should not be really necessary in level 2 missions if you have halfway reasonable skills.
[Caracal, Caracal fit]
Ballistic Control System II
Ballistic Control System II
Large Shield Extender II
Large Shield Extender II
Adaptive Invulnerability Field II
Adaptive Invulnerability Field II
10MN Afterburner II
Light Missile Launcher II, Scourge Light Missile
Light Missile Launcher II, Scourge Light Missile
Light Missile Launcher II, Scourge Light Missile
Light Missile Launcher II, Scourge Light Missile
Light Missile Launcher II, Scourge Light Missile
Medium Core Defense Field Purger I
Medium Core Defense Field Purger I
Medium Core Defense Field Purger I
Warrior II x2
Low-level missions are not very lucrative, but you still shouldn't make a loss on them if you are doing them properly. Level 3 missions should earn you okay money, but to make a reasonable amount of money for your time you need to fly level 4 missions.
If you fly a shield-tanked ship (I assume you're still flying a Caracal), you shouldn't let yourself get shot into armor. Just warp out and dock at a station to fill up your shields quickly again. Your only cost should be your ammunition. Some missions are harder, and you'll have some difficulties in the beginning when you're still learning, but if you have that much trouble in most missions you're doing something wrong.
You should learn about fitting your ship properly, making mistakes there can make a huge difference. Your skills also matter quite a bit in the beginning, even with only one or two weeks more worth of skills it'll get a lot easier. Make sure to have your main ship skill and your weapon skill at 4, basic shield skills and weapon skills at 3-4. Read mission reports on EVE survival to learn the triggers of the missions, that will help you to avoid aggroing too many enemies at once.
I'm keeping this a bit vague as there are whole guides written about these topics. I'd recommend to just read up on the basics of EVE combat and the missions should get far easier quickly. And don't mind losing money on the level 2 missions, train up for a Drake and try out the level 3 missions once you have the necessary skills.
Best Answer
Oh, that's easy.
What you do, is you take that ore and you process it into minerals!
Those minerals will sell much faster and in higher quantities than the equivalent ore.
You might say "oh, that's such a bother, I don't really want to do that". Well, guess what? Neither does the purchaser. That's what they're buying when they buy minerals, the convenience of not having to process raw materials into the minerals they really want.
As usual, scout the market (and perhaps the nearby markets, Tash-Murkon is close to Amarr) and have a look at what the daily quantities traded are and you'll have an idea of how much you can move for what price how quickly. Everything changes at the region boundary.