Specific Beats General - A permanently polymorphed creature will stay morphed if it dies

In 5e, you always apply a general rule unless there is a specific exception. That is exactly what is happening in this case. Generally, the target will revert after the full duration, upon the target reaching 0 hp, or upon dying. However, there is a specific exception for when the caster concentrated on the spell for the whole duration. In that case, the change lasts until dispelled, full stop. The first sentence no longer applies in this case, because the second is an exception to it. As a result even if the conditions in the first sentence are met, the creature stays transformed because of the second sentence.

"Until the target drops to 0 hit points..." isn't enough because of effects that can instantly kill a creature without affecting hit points. These effects are usually high level magic like the 9th level Power Word: Kill and the 7th level Divine Word both of which can instantly kill a creature without changing their hit points at all, as long as the creature's current hit points are within a certain threshold. In these cases, you do not drop to 0 hp; instead you just immediately die.

Yes you can true polymorph into an ancient brass dragon

As you say, the spell and rules are clear. An ancient brass dragon is a creature, it is not a shapechanger (and may not matter if they were), and it is of the appropriate CR for your level.

Thus, there is no reason why you would not be able to use true polymorph in this way.

Ancient Brass Dragons are not shapechangers

Ancient Brass Dragons are not considered shapechangers. A creature is a shapechanger if they have the monster subtype (Shapechanger). Ancient Brass Dragon's creature type is dragon.

The fact that it is able to change shape (a special ability) is irrelevant to being able to transform into that shape. The dragon does not have the shapechanger subtype, thus it won't be potentially conflicted with the shapechanger subtype restriction.

You can use all the abilities of your True Polymorph form

The target’s game statistics, including mental ability scores, are replaced by the statistics of the new form.

Jeremy Crawford says:

When a game effect, like Wild Shape, says you use a creature's statistics, you use its stat block (see "Statistics," MM, 6).

According to that same section "Special Traits, Actions, and Reactions" are part of a monster's stat block.

Ability to change shape back to your old form is unclear.

It is worth noting that you may not be able to use change shape to change back into your old form: Can you use a Dragon's Change Shape Ability to Turn Back Into Yourself?