I'm... not sure where you got the idea that a long bow can fire twice as fast as any other weapon. That's simply not true.
Your rate of attack is determined solely by your base attack bonus unless there's a special effect that specifically says it gives you additional attacks. Yes, you are correct; +6/+1 indicates that the Ranger can make two attacks, one at +6 and one at +1 (plus any relevant ability modifiers, attack modifiers etc).
Your Ranger player might have the Rapid Shot feat, which specifically indicates that you can make an extra attack during a full-round attack action if you take a -2 penalty (I believe; not looking at the rules just now) to all attacks you make that round. This would mean he could attack twice before level 6, which is when you get a +6 BAB and two attacks. If your Ranger has +6/+1 attacks and Rapid Shot, he could fire three times in one round with a -2 to all attacks.
Moving on to full-round actions, I can't think of any weapon, feat or anything else that gives the player the ability to attack more than once in a standard action off the top of my head except for a two-weapon fighting feat (and I might have misremembered that). Even with Haste you still need to take a full-round action to make use of the extra attack it gives. If you want to take advantage of your full range of attacks that you have, no matter what level you are, you must take a full-round action, at which point you can use all of the attacks separated by slashes in your character's BAB.
The "Rate of attack" thing you mentioned reminds me of AD&D, however, where darts had three attacks per attack action. Me and my buddy had some pretty funny discussions about an ogre that threw large-sized darts. Those days are long gone, however (unless you decide to switch systems).