Fired a bullet upwards, can it fall down and kill me? I know that if something is thrown up with a velocity v, it comes down with the same velocity as long as its motion faces no resistance. So is it possible for me to fire a bullet and be killed if it drops down on me directly? Assuming there is no air resistance. 
 A: Yes the bullets can fall down and injure or kill you. In fact in countries were celebratory gun firing is possible people are often injured by falling projectiles. 
Shooting straight up is less dangerous than at an angle because the terminal velocity is much lower than the muzzle velocity of the projectile. 
When shooting at an angle some of the horizontal motion tends to be conserved making the bullets velocity when it falls back substantially higher.
https://en.m.wikipedia.org/wiki/Celebratory_gunfire
This article covers this in more detail
Now how fast would the bullet hit you when coming straigt down? Assuming it reached terminal velocity, its speed would depend on its mass and surface area.
$v_{terminal}=\sqrt{2mg/C \rho A}$
The density and drag coefficient of air are assumed to be constant at 1.29 $kg/m^3$ and 0.5 resepectively. If the bullet weighs 30 grams* and has a classic caliber of 9 mm, then the terminal velocity would be
$v_{terminal}=\sqrt{2*0.03*9.18/0.5*1.29* 0.009^2\pi}$
$=58.9 ms^{-1}$
Even a weak a very standard rifle has a muzzle velocity twice that value as seen here:
https://en.wikipedia.org/wiki/Muzzle_velocity
*averaged mass of bullets as given by the source:
http://hypertextbook.com/facts/2000/ShantayArmstrong.shtml
A: There is always air resistance, unless you are in space. If there was no air resistance, a bullet would land at the same speed it was shot at.
On Earth, a spent bullet is rarely lethal. In big wars (like World War II) it was common for soldiers to get hit by spent bullets. Normally they will hit you and fall away, causing just a bruise,
An unlucky hit could kill a person. For example, if a falling bullet hit a person directly in their head and it was a hard jacketed bullet and the point happened to contact the skull first, it might penetrate and kill. Usually this will not happen, either because it will hit at an angle, or the bullet (which tumbles) makes contact on its side, not the point...
