^{please note that I only skimmed through the code, so I might be missing something}

First, take the sprite without rotation. You decide on some coordinates (x, y) that is the origin for bullets.

Now, when the ship rotates, the coordinates for this origin point should also rotate. The relevant equations are:

x' = x cos(angle) - y sin(angle)
y' = y cos(angle) + x sin(angle)

Where (x', y') are the new coordinates of the point after the rotation by "angle". Please note that these equations are for the Y axis going up, like in standard math. On the computer screen, it's usually the other way, so you'll have to switch things around a little.
They also assume that you are rotating about (0,0), which might not be the case. If you're rotating about (u,v), you just add (u,v) to your (x,y), do the rotation, and then subtract (u,v) from (x', y').

About your itofix question, I'm not sure what is it that you have a problem with. itofix converts an "int" into a "fixed". Your angle variable is already a "fixed", so you can use it with fix***() functions right away.

I strongly encourage that you just forget about fixeds, especially if you're learning. They'll just mess with your head. If you want to use them though, read the section of manual pertaining to them thoroughly.

Anyway, I'm sure none of this makes sense, so wait until someone comes and translates .

Radians make this sort of thing much easier.

I can't really tell what your code is trying to do... Wish I had more time to read over it, but I believe it's similar to what's happening in this post.

Okay, radians are 0 to pi*2 for a full rotation. The rotate_sprite function does require a fixed however, so lets deal with that first.
rotate_sprite(bmp,sprite,ship.x,ship.y,ftofix(ship.angle*128.0/M_PI));

As for the bullet's initial position and velocity,

Nope:

Nope, you're simply going to change spawn_distance to the maximum width or height of your image. So spawn_distance=31; (May want to go with 32 to make it a little safer when finding it he bullet has hit anything)

Sorry, I wasn't quite thorough in explaining the starting x and y of the bullet. Simply start at the center of your ship, move it to the outside of the ship, then set it's velocities. Something like:

temp_bullet.x=player_ship.x+spaceship->w/2+spawn_distance*cos(player_ship.angle);
temp_bullet.y=player_ship.y+spaceship->h/2+spawn_distance*sin(player_ship.angle);
//...then the velocities the same as before

Side notes:
Your definition of PI is unnecessary. Simply call M_PI

Using iterators with vectors will considerably speed up your program. I'd change this block

if(bullet.empty() != true)
  {
    for(int i = 0; i < bullet.size(); i++)
    {
      bullet<i>.x += bullet<i>.vx;
      bullet<i>.y -= bullet<i>.vy;

      if(bullet<i>.x > x_res || bullet<i>.x < 0 || bullet<i>.y > y_res || bullet<i>.y < 0)
        bullet.erase(bullet.begin() + i);
    }
}

To

for(vector<Projectile>::iterator i=bullet.begin(); i!=bullet.end(); i++) {
  i->x+=i->vx;
  i->y-=i->vy;
  if(i->x > x_res || i->x < 0 || i->y > y_res || i->y < 0) {
    //This simply swaps the bullet that needs to be deleted
    //with the last element in the vector and deletes it.
    //Much faster than resizing the entire vector.
    if(i<bullet.size()-1)
      memcpy(&bullet<i>,&bullet.back(),sizeof(bullets));
    bullet.pop_back();
  }
}

Ok, using Ceagon's formulas(with some modification, for some reason the point was 64 radians(90 degrees) over what it should have been...) it works. When I first looked into how to go about getting rid of the bullets that went out of range I was going to use an iterator, but I have no experience with them. As such, I cannot decipher what is wrong with these two lines, even after extensive searching and reading .

if(i < bullet.size() - 1)
     memcpy( &bullet<i>, &bullet.back(), sizeof(bullet));

Heres all of my current code.

When it gets down to the last bullet in the vector the program now crashes with a "instruction at <insert address here> referenced memory at <insert address here>. The memory could not be 'read'." I'm guessing the iterator doesn't like all the erases?

EDIT: Nvm, every time I go to reply your post has been updated heh...

Yea, the second one crashes after 4 or 5 bullets exit the screen. Was about to say first one was also buggy until I noticed the increments location changed as well... Actually, the second one works now that I noticed that.

So for everytime I need to cycle through a vector similar to this and possibly remove certain elements should I use that code?

Example of implementation for a lifespan for projectiles(Didn't want to repost entire source so I started at while and cut it off right after if(!bullet.empty())'s closing brace).

         while( speed_counter > 0)
         {
                if(!bullet.empty())
                {
                     for(std::vector<Projectile>::iterator i = bullet.begin(); i != bullet.end();)
                     {
                          i->lifetime++;
                          if(i->lifetime >= i->life_max)
                          {
                               memcpy(&(*i),&bullet.back(),sizeof(Projectile));
                               bullet.pop_back();
                          }
                          else
                               i++;
                     }
                }

EDIT: Nvm, just added in an extra check and variable increment to the existing for loop.