Characters are defined as General, Battle Standard Bearer, Hero, Champion (and equivalent figures to heroes and champions, such as Plague Priests and Wardancer champions), Magic Users and in most cases, Assassins. As a general rule, if you pay "character points" for it (see your army book if you are unsure), it is subject to the special rules for characters.

As a general matter, it is good to remember that characters suffer the same fate as the units in which they are placed - they may not leave a unit when it breaks, nor may they attempt to rally when their unit is smaller than 25% of its original size. Moreover, with the exception of champions, characters do not gain the special abilities of the units in which they are placed - thus a character placed with a unit that is immune from breaking will still have to take break tests. Keeping these rules in mind will help avoid many rules disputes.

The 5th edition rules went a long way towards resolving any ambiguities in this area. If a unit suffers a psychological failure or breaks, any characters with that unit are subject to that liability, even if they would have been otherwise immune to it. Conversely, if a character is liable to a psychological rule or break test that the rest of the unit he is placed with is immune to, he must make any appropriate tests on his own and suffer the consequences alone, if he should fail.

The different Chaos champions of Slaneesh have a special rule that allows them to stay in hand-to-hand combat when the unit that they are in breaks. This is an exception to the general rule stated above.

No.

As a notable exception Assassin (Skaven and Dark Elf) characters have a special rule that allows them to leave fleeing units.

Just like everybody else, characters can only charge a target they can see. In Warhammer, regiments and individual models can only see 90 degrees to their front, so if a unit is outside this arc they are safe.

When the Battle Standard Bearer character is killed. The Battle Standard Bearer is considered a character, and all of the character targeting rules for missile fire, hand-to-hand combat, and magic spells apply.

No. The battle standard allows units within 12" to re-roll failed break tests; it does not allow re-rolls for failed panic, fear, or terror tests.

No.

No, characters are always placed in the front rank, unless the unit is in combat on another side.

Yes, and yes. Note, unlike earlier editions, in 5th edition this rule is not based on a rank and file member physically pushing the character out of the way, but merely giving him a warning shout.

Yes and No. Whether a mounted character can be singled out for missile fire depends on his size relative to the size of the unit rank and file.