Yes it is a composite long bow for a 15 strength that is why the +2 I know I have forgotten about that at times that I get that +2 for damage. I need to update my character sheet so I take all of this into consideration when I roll. Thanks for the heads up.
Poop, I was afraid it was a Strength Rating +2 (Requires a 14 Strength, not 15, so that's lucky at least). You only get that +2 to damage if your Strength modifier is +2. Since your Strength is a 13, your modifier is only +1. You still get to add that +1 to damage, but until you get a 14 Strength (Which would give you a +2 modifier), you actually take a -2 to your attack rolls since your modifier isn't equal to or greater than the bow's Strength Rating.
Bow Attacks within 30 feet: +6 (BAB) + 1 (Dexterity 12 = mod +1) - 1 (Rapid Shot is -2, but your gem is awesome) + 1 (Point-Blank Shot, I'm assuming you have it since it's a requirement for Precise Shot) + 1 (Masterwork bonus for weapons) - 2 (Wielding a Composite Longbow with a Strength Rating 2 when your Strength is less than 14 - might consider upping your Strength by 1 when you hit level 8, since this would get rid of that problem by giving you a 14 Strength) = + 6 total.
If you make a full-attack action with your bow within 30 feet of the enemy, + 6 / + 6 / + 1. Just remember that your first shot actually fires two arrows, so you should roll damage four times, not three. If the first shot hits, the extra arrow fired with it (Manyshot) also hits and if it misses, they both miss.
Damage within 30 feet: 1d8 + 1 (Your Strength modifier, up to the bow's Strength Rating) + 1 (Point Blank Shot) = 1d8 + 2
Outside of 30 feet, your full-attack action would give you a + 5 / + 5 / + 0 to hit and you would do 1d8 + 1 damage for each attack that hits (Again, remember the first shot fires an extra arrow).
If you ever want help with a character or find something confusing, just let me know. I enjoy building characters just as much as I do playing! I wish I could share some of the characters I've built, but writing them all out instead of sharing a link to their page just isn't something I feel like doing today .
Wait, stop the presses! I just checked the points and realized that you don't have your +2 to any one ability for being a Half-Elf applied to your stats! Is that why you mentioned the 15 Strength earlier? If so, you might want to update your character sheet to reflect that. It'll also change my numbers listed above.
Within 30 feet: Attack = + 8 / + 8 / +3. Damage = 1d8 + 3.
Outside of 30 feet: + 7 / + 7 / + 2. Damage = 1d8 + 2.
Edited: Diarmadhim on 7th Jun, 2016 - 5:23am
Yeah, I checked and saw that while your character sheet says 13, you had mentioned 15 and I didn't see the points spent. That last blurb of mine is right "Within 30 feet: Attack = + 8 / + 8 / +3. Damage = 1d8 + 3. Outside of 30 feet: + 7 / + 7 / + 2. Damage = 1d8 + 2."
Just looking out to make sure you're getting everything you're supposed to .