Yes
No, TWF gives one extra attack. To get more off hand attacks, you have to take Improved/Greater TWF.
No, it grants a 3rd attack at +6 w/normal modifiers and all attacks take -2 penalty
Yes, the /+1 grants you a second attack at -5 to hit but only as a full attack action. You only ever get one attack as a standard action (barring other special abilities)
Two weapon fighting only grants you a single additional attack. you need improved (and greater) 2 weapon fighting to gain a 2nd (and 3rd) off hand attack.
With rapid shot you do indeed get three attacks, but the extra attack is at your highest BAB and all are at -2 (so +4/+4/-1 plus all other modifiers).
When your BAB reaches +6/+1 here are the breakdowns:
(Assuming a 16 Str (+3 bonus) on melee attacks and 16 Dex on ranged, no other modifiers for simplicity).
One weapon only:
You have two attacks, the first is +9 (6+3) and the second is +4 (1+3).
Two-Weapon Fighting Feat (Assuming off-hand weapon is light):
You will have three attacks with the following bonuses: +7 (6+3-2, main weapon), +7 (6+3-2, off-hand weapon), and +2 (1+3-2, main weapon).
If you also have the Improved Two Weapon fighting feat, you will get that fourth attack which comes from your off-hand weapon at a +2 bonus as well.
Rapid shot will be similar to the two-weapon fighting feat as you will have two attacks at +7 (6+3-2), and a third attack at +2 (1+3-2).
Hope that helps break it down easier.
A few questions on this. Sorry if this has been covered before.
6th level BAB is +6/+1, does the +1 grant a second attack to a PC +1(+ all other normal mods; i.e. abilities; magic weps etc.)?
If so, does using two-wep fighting figure to be 4 total attacks w/ normal added modifiers?
Also the Feat Rapid Shot grant a 3rd attack at +1 w/ normal added modifiers?
IMPOSTER!!!!!
Just kidding.
Yes the +1 of a +6/+1 BAB grants a second attack.
If Two-Weapon fightin you will get three attacks at +6/+6/+1 with all of the appropriate modifiers for twf, feats, abilities, etc...
Yes Rapid shot gives you 3rd attack with all of the appropriate modifiers.