What will happen when a Wood elf with the Hunters Talon shoots one of them down? Does the unit loose the banner and/or instrument, or does someone else pick it up behind/next to him?

If it works like killing them in combat, someone else picks it up and carries on. Unless the Hunters Talon says otherwise- I've no idea what it does.

Yeah, I think Bigbee is right, unfortunately.

But you can still kill the champion.

You cannot specifically pick out a Standard bearer or a musician to shoot at- they are the exact same as any rank and file troop. All casualties caused to a unit cause for the troops to be removed from the back, which basically shows the next warrior stepping forward to fight.

The Hunter's Talon allows its bearer to aim at a specific miniature in an unit.

You might kill the standard bearer, but a similar model is supposed to pick it up. As a rule of thumb, you can only target models with different stats.

You can target a BSB, though. But with one single S3 attack, you don't have a very good chance to make a difference. A bow is virtually useless for or against a character.

In other words - no, you can not kill standard bearers or musicans :).