Going to give you a few quick answers. Much more can be found online... I'll see if I can find you some references tomorrow.
1 movement doesn't matter 95% of the time. A player or NPC's accuracy is based on stats. However some attacks have a maximum range and some attacks will affect targets within a certain range of an attack area. if you see a weird symbol on the ground or other animation... Lightning, earth shattering, ect... that denotes an area attack (also called an AOE attack) and you should probably move away from it if it causes you damage. The only time movement really matters in MMO fights is positioning to avoid enemy attacks (to the extent possible) while maximizing your attacks. In operations and flash points you may have to move in and out of a certain range (also called "jousting") to fight bosses.
2 covered by above.
3 you need to repair your equipment periodically to keep it from breaking. You can do this at any vendor (even medical droids) except for class trainers. When you look at the vendor window there is a tab for repairing equipment. Additionally at the bottom left of the vendor window is a button labeled "repair all". This will repair all damaged equipment. You should use the repair all most of the time... I can only see repairing equipment individually if you are very low on credits. Your blaster is probably broke from damage and not overheating... Heat is a separate mechanic similar to power or mana from what I understand.
Thanks man, great info!