Finally a few days ago, I managed to draw my first line, my thanks go to "Butsi" who had the patience to put me on the right path.
Updated topic start, code Solution:
public static void drawBoundingBox(Vec3d player_pos, Vec3d posA, Vec3d posB, boolean smooth, float width) {
GL11.glPushAttrib(GL11.GL_ENABLE_BIT);
GL11.glDisable(GL11.GL_CULL_FACE);
GL11.glDisable(GL11.GL_LIGHTING);
GL11.glDisable(GL11.GL_TEXTURE_2D);
GL11.glEnable(GL11.GL_BLEND);
GL11.glBlendFunc(GL11.GL_SRC_ALPHA, GL11.GL_ONE_MINUS_SRC_ALPHA);
GL11.glTranslated(-player_pos.x, -player_pos.y, -player_pos.z);
Color c = new Color(255, 0, 0, 150);
GL11.glColor4d(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha());
GL11.glLineWidth(width);
GL11.glDepthMask(false);
Tessellator tessellator = Tessellator.getInstance();
BufferBuilder bufferBuilder = tessellator.getBuffer();
bufferBuilder.begin(GL11.GL_LINES, DefaultVertexFormats.POSITION_COLOR);
double dx = Math.abs(posA.x - posB.x);
double dy = Math.abs(posA.y - posB.y);
double dz = Math.abs(posA.z - posB.z);
//AB
bufferBuilder.pos(posA.x, posA.y, posA.z).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //A
bufferBuilder.pos(posA.x, posA.y, posA.z+dz).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //B
//BC
bufferBuilder.pos(posA.x, posA.y, posA.z+dz).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //B
bufferBuilder.pos(posA.x+dx, posA.y, posA.z+dz).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //C
//CD
bufferBuilder.pos(posA.x+dx, posA.y, posA.z+dz).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //C
bufferBuilder.pos(posA.x+dx, posA.y, posA.z).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //D
//DA
bufferBuilder.pos(posA.x+dx, posA.y, posA.z).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //D
bufferBuilder.pos(posA.x, posA.y, posA.z).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //A
//EF
bufferBuilder.pos(posA.x, posA.y+dy, posA.z).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //E
bufferBuilder.pos(posA.x, posA.y+dy, posA.z+dz).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //F
//FG
bufferBuilder.pos(posA.x, posA.y+dy, posA.z+dz).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //F
bufferBuilder.pos(posA.x+dx, posA.y+dy, posA.z+dz).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //G
//GH
bufferBuilder.pos(posA.x+dx, posA.y+dy, posA.z+dz).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //G
bufferBuilder.pos(posA.x+dx, posA.y+dy, posA.z).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //H
//HE
bufferBuilder.pos(posA.x+dx, posA.y+dy, posA.z).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //H
bufferBuilder.pos(posA.x, posA.y+dy, posA.z).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //E
//AE
bufferBuilder.pos(posA.x, posA.y, posA.z).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //A
bufferBuilder.pos(posA.x, posA.y+dy, posA.z).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //E
//BF
bufferBuilder.pos(posA.x, posA.y, posA.z+dz).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //B
bufferBuilder.pos(posA.x, posA.y+dy, posA.z+dz).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //F
//CG
bufferBuilder.pos(posA.x+dx, posA.y, posA.z+dz).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //C
bufferBuilder.pos(posA.x+dx, posA.y+dy, posA.z+dz).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //G
//DH
bufferBuilder.pos(posA.x+dx, posA.y, posA.z).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //D
bufferBuilder.pos(posA.x+dx, posA.y+dy, posA.z).color(c.getRed(), c.getGreen(), c.getBlue(), c.getAlpha()).endVertex(); //H
tessellator.draw();
GL11.glDepthMask(true);
GL11.glPopAttrib();
}