GMs call on all of these since they don't specify exactly how they interact.
Precise Bombs with either Strafe or Breath Weapon Bomb: I can see this working quite well: effectively you can ignore certain squares from the line or cone. Not horribly broken since the cone or line can usually be aimed to not hit allies anyway. I'll allow it.
Breath Weapon Bomb and Strafe Bomb: This one is more difficult since both abilities change the bombs area. I am leaning towards no since it raises too many questions on how they *could* work. e.g. line that damages everyone as if a direct hit and then reflex for half, or a cone that damages everyone as if it was a direct hit and the line only does splash damage, or one square in the line deals damage as if a direct hit and everyone else including the cone take splash damage, or or or...
Precise bombs is always usable, unless explicitly mentioned otherwise. Yes, it makes it a little odd that you can "skip" parts of the line to avoid hitting allies, but RAW it works just fine.
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Discovery (Su): At 2nd level, and then again every 2 levels thereafter (up to 18th level), an alchemist makes an incredible alchemical discovery. Unless otherwise noted, an alchemist cannot select an individual discovery more than once. Some discoveries can only be made if the alchemist has met certain prerequisites first, such as uncovering other discoveries. Discoveries that modify bombs that are marked with an asterisk (*) do not stack. Only one such discovery can be applied to an individual bomb. The DC of any saving throw called for by a discovery is equal to 10 + 1/2 the alchemist's level + the alchemist's Intelligence modifier.
Precise bombs: Whenever the alchemist throws a bomb, he can select a number of squares equal to his Intelligence modifier that are not affected by the splash damage from his bombs. If the bomb misses, this discovery has no effect.
( no * , so you can add it whenever )
Strafe Bomb (Su): The alchemist can throw bombs that splash in a 40-foot line rather than affecting a radius. The line starts at the alchemist and extends away from him in the direction he chooses. The alchemist designates one creature in the squares affected by the line to be the target of the bomb and makes his attack roll against that creature; all other squares in the line take splash damage. If the alchemist has the explosive bomb discovery and throws an explosive strafe bomb, the line of splash damage is 80 feet long instead of 40 feet.
( no *, so you can use it whenever )
Breath Weapon Bomb*: Instead of drawing the components of, creating, and throwing a bomb, the alchemist can draw the components, drink them, mix them within his body, and then expel them as a breath weapon as a standard action. This breath weapon is a 15-foot cone and has the same DC as the bomb. Each creature within the cone takes damage as if it had suffered a direct hit from the alchemist's bomb, but succeeding at a Reflex save (DC = 10 + 1/2 the alchemist's level + the alchemist's Intelligent modifier) halves the damage. Unlike throwing normal bombs, drawing, drinking, and expelling breath weapon bombs does not provoke attacks of opportunity. An alchemist must be at least 6th level before selecting this discovery.
( *, so you could choose Acid Bomb, or Explosive Bomb, or Breath Weapon Bomb, but not two or more of those. )
so yes, you can.
drink it and choose to spit out a line of bomb, instead of a cone of bomb. and everyone in it would take direct hit damage, with a reflex save for half, however since Breath Weapon Bomb deals direct damage to all creatures, and splash damage to none, Precise Bombs wouldn't help you: everyone, even allies would need to save vs. full damage.
you can combine them, it just doesn't do what you expect, I think.