There should be numbers next to missions indicating their difficulty (1, 2, 3 etc). Stick to level 1 missions and get some greens and purple level gear. Also make sure you have a loadout that can deal with armored guys like dreadnoughts. I usually run with a bolter and plasma, grav, or melta gun. Not the heavy versions, but it's all preference. Anyways as you gear your character their Attack and Defense values rise, which should be shown on the character sheet where all your stats are. I'd just mostly run level 1 until it is too easy then move on.

You'll have to hit and run sometimes, mostly when dealing with dreadnoughts or other similarly big armored enemies. The armor which gives you the sentry gun ability can be helpful. You will likely also run into an enemy that likes to spawn waves of nurglings, so charge that guy and take him out quick or you'll have a real bad time.
 
You can crush enemies with debris destroying pillars. Easiest just to throw a grenade at the pillar. 

No worries! 

When you select a weapon in your inventory you should see a box pop up with basic details and four abilities. Mouse over any of the four abilities the weapon has and another box pops up with a description of the skills specific effects, damage values and damage types etc. That's where you should see armor piercing if the weapon has it.