When I reach level 6 my BAB will be +6/+1. When I make my actual attack with weapon focus (+1) and strength mod (+3) does it make it +10/+5?
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Your Base Attack Bonus is +6/+1 if you have six levels in a Full BAB class. This doesn't change.
Your Attack Bonus, on the other hand, will be your BAB + Str modifier + other bonuses, in this case 6+3+1, as you thought. Iterative attacks are at -5, so yes, your total attack bonus on a full attack is +10/+5.
Not exactly. Your Base Attack Bonus (BAB) is your base attack bonus - it is solely the attack bonus granted by all your classes, and nothing more. Feats and modifiers don´t change that value.
However, you don't use JUST the BAB on your attack rolls. An attack roll is the sum of your BAB with all the appropriated bonuses and penalties. This is called Total Attack Bonus or just Attack Bonus.
So, let´s suppose that your BAB is +6/+1. Your Attack Bonus with the weapon that you have Focus will be +6 (BAB) + 1 (Weapon Focus) + 3 (your Str modifier) = 10. Since you have a second attack, it will just follow the math: +1 (BAB) +1 (Weapon Focus) +3 (Str Mod) = 5.
Keep in mind that having a huge attack bonus don't give you extra attacks the same way having a huge BAB will. If your BAB is +7/+2, for example, and you put up the same feats and modifiers, you will get a total attack bonus of +11/+6, but that +6 wont give you an additional attack. You will only be able to do extra attacks if your lowest BAB is 6 or higher.
Yes. Weapon focus gives its bonus to all attacks with that weapon. Strength gives its bonus to all strength-based attacks (which is all regular attacks unless you use weapon finesse or some other odd ability).
So with your preferred weapon it's going to be +10/+5. If you pick up a different kind of weapon, it's +9/+4. If you pick up a ranged weapon and your Dex mod is +2, it's going to be +8/+3.
Also, you even get this secondary attack when you multiclass; if you get +4 BAB from one class and +2 BAB from another, you still end up with +6/+1.