Feats to increase number of bomb attacks per round in Pathfinder

In normal circumstances, Alchemist can throw one bomb per round. But there are at least 3 feats that should increase the frequency:

1. Fast Bombs

An alchemist with this discovery can quickly create enough bombs to throw more than one in a single round. The alchemist can prepare and throw additional bombs as a full-round action if his base attack bonus is high enough to grant him additional attacks.

2. Rapid shot

When making a full attack with a ranged weapon, you can fire one additional time this round at your highest bonus. All of your attack rolls take a –2 penalty when using Rapid Shot.

3. Two weapons Fighting

If you wield a second weapon in your off hand, you can get one extra attack per round with that weapon.

So far I've heard that :

a) Only Fast Bomb works

b) Only Fast Bombs and Rapid Shot... but apparently not always

c) All of the above work, but TWF works only after you get Fast Bombs

So how it is in the end? How to increase number of attacks per round? Are bombs treated as ranged, melee weapons or maybe as spells?

Per the tabletop rules, rapid shot and two-weapon fighting work, but only if you have fast bombs. Source

The reason for this is, that bombs are a ranged attack, but unless you have fast bombs, you cannot do a full attack with bombs and without a full attack you cannot attack multiple times, thus TWF and RS don't work.

However, the implementation of this bugs out quite often as of pre 1.1 versions (haven't played since then). Don't know, whether it's fixed yet, in any case, if everything works correctly: TWF and RS should work, if you have fast bombs and shouldn't, if you do not.