The short answer: practice. The long answer: You might need a private instructor to make sure your technique is good. While taking private lessons, you need to practice the fundamentals: scales, lip slurs, etc. Then when you are practicing your music, you need to practice it perfectly. Meaning, get a measure perfect before running through the piece. If you are making a mistake - stop and fix that mistake until you can play it perfectly 4 or 5 times in a row. Remember the words of Vince Lombardi: Practice doesn't make perfect - perfect practice makes perfect. If you practice it wrong, you will always get it wrong.
The trumpet is part of the brass section.
The Flute is in the Woodwind section/family and the Trumpet is in the Brass section/family.
Trumpet is in the brass section.
Yes, the trumpet 1 part is normally harder than trumpet 2 or 3 and normally the best player or players play on the first trumpet part.
A "trumpet player" can be called a trumpeter. :)
brass section that's on the right.
Are you sure you mean Art Blakey? To the best of my knowledge, he was a jazz drummer, not a trumpet player.
The cast of The Trumpet Player - 2014 includes: Franklin Killian as Trumpet Player
If you mean getting signed as a professional player, it's difficult. There are thousands and thousands of aspiring trumpet players out there, and most of them aren't as good as they think they are. For symphony orchestras, you almost always have to audition, and many symphonies don't have regular audtions. For instance, the trumpet section in the symphony in my city has been the same for 5 or 6 years, and the principal trumpet player has been the same player for 20 years.