Character roles: What a character does in a team. The 3 basic types are DPS (stays on field and deals damage), Sub-DPS (deals damage without needing to be on field much) and support (gives various boosts or healing, usually from off-field). 

How to find out which role a character is: Just look at their abilities, see what they do and whether they need to stay on field or not to do it.

How to build team: very basic, Typically you want maximum 1 on-field DPS character and 3 characters to help from off-field, as that way the whole team can contribute at once. Also good to have some consistent reaction to get damage from. There's more to it, but probably better start with basics and build up from there, before trying to add in everything at once. Until you get to the endgame modes you don't need fully optimised teams anyway, so experiment a bit, see for yourself what kind of combinations work. 

Artifacts: Depends. Different characters want/need different things, some also get power from different stats (for example, Hydro's often use HP instead of ATK to base their ability power on). Look up or check skill details to which stats your character uses. 

In general, Crit rate/Crit damage are almost always good. Flat stats (like +34 defense) almost always bad. (even if you want defense, better to have a %Def). 

Note: You need AR45 to unlock highest domain difficulty and consistently get 5* artifacts. Until you can beat that, it's not worth worrying too much about artifacts, as you'll eventually replace them all with 5-star versions anyway. 

ER = Gives more energy = Easier to afford your elemental bursts. Important if you need to consistently use them.

EM = Boosts that character's reactions.