the trumpeters
It's Israfil
The abstract noun of the idiom "blowing one's own trumpet" is "self-promotion" or "self-aggrandizement." This refers to the act of boasting or bragging about one's achievements or abilities, often to gain recognition or praise. Such behavior emphasizes an individual's desire for validation or acknowledgment from others.
by air blowing into them
These are the angels heralding the breaking of each of the seals upon God's wrath, with a trumpet. basically , God's wrath is sealed away til judgement day, and before that time the 7 seals will be broken and a tribulation (great suffering) for each will occur, and when the seal is broken the angel signals it by blowing his trumpet.
by blowing through the mouth peice
You buzz your lips, which causes the trumpet to vibrate. You change notes by pressing valves or blowing the air faster.
Free blowing means that the trumpet doesn't feel stuffy when you play it. I'm not really sure how to explain it, other than comparing this: imagine blowing air through a soda straw, then blowing air through a water hose. The water hose is bigger and will allow you to blow larger amounts of air through it.
By blowing more air into it faster and harder
Abstract nouns that may represent the term 'blowing one's own horn' are promoting, boasting, or bragging. These are words for a concept.
The trumpet is made of brass tubing and the sound is produced by blowing air through it. The xylophone is made of wooden bars and the sound is produced by striking them with mallets.
I once read a story about this. It's an elderly bearded man riding through the streets in Israel blowing his trumpet to let the children know it's time for Shabbat.