Generally yes; the sole exception is that the fighter will often target flak frigates for some reason.  Generally the most important management is to keep fighters, bombers, and light frigates clear of danger.  These units are somewhat fragile so you need to maneuver them around dangers to keep them alive.

1) Is it possible to attack target by type? Eg. I want my fighter squadron to attack 3 bomber squadrons. How do I select the targets so that the figher squadron will attack all the bomber squadrons without Shift-Right-Clicking all the different bombers squadrons?

2) When the units are displayed in stacks of 20 on the left panel, and I do a right click on it, does my unit attack all the 20 units in the stack or just one unit?

Thanks!

Yes this is one of the to do list for next patches i believe. 

Your units most of the time focus fire on one ship but not 100% of the time. And when that ship is killed they go back to the script (read prefer and attack ship set up by devs) and you need to set command again.

Yes you can but if you have them stacked by 10 they will attack only 1 st ship and then move on. They won't go throught all 10 ships and then attack what you selected next....