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First of all, this character is an 11th level Slayer.
If you want to use a Crossbow effectively, you will need to take 5 levels in the Bolt Ace Gunslinger. Once you have five levels in Bolt Ace you have every class feature that matters and you should multiclass out to something else (Slayer would be a great choice).
So definitely rebuild into a Bolt Ace 5 / Slayer 6 if you can.
First of all, I wanted to make this character permanently enlarged so his size would be Large (especially since it is relatively cheap, costing only 2500gp).
Increasing your size category is very bad for ranged characters, and the small increase in damage is not worth the hefty penalties you take. Melee weapons get the benefit of increased threat range for being large-sized, but ranged weapons get no equivalent bonuses. Given the hefty accuracy penalty you take, it's not worth it.
However, there exists a feat called Lighten weapon ,a combat feat from Kobold Press (http://www.d20pfsrd.com/feats/3rd-party-feats/kobold-press/combat-feats-3r d-party-kobold-press/lighten-weapon-combat/) . This reduces the effort to wield bigger weapons than your size would allow so it would theoretically allow the character to wield Huge size weapons.
Lighten Weapon either causes you to take a -2 penalty to attack, or forces you to pay a second feat to avoid the penalty. Either way, you're getting ripped off. There are some very specialized builds that multiply their damage dice that can utilize feats like these, but you need to start with something like a greatsword to make it workable. I don't see this feat working out for a crossbow build.
I have chosen the feats Two weapon fighting, improved two weapon fighting, greater two weapon fighting, deadly aim, lighten weapon (crossbow) and Improved Lighten Weapon (so the -2 penalty for lighten weapon doesn’t occur anymore). The slayer talents I chose were all from Ranger combat style (crossbow mastery, rapid shot, Point Blank shot, Precise shot and rapid reload). The advanced slayer talent I chose was Assassinate. Crossbow mastery is especially useful since I can reload any type of crossbow as a free action.
You can only take Ranger Combat style talent three times. Crossbow Mastery can be dropped, but you absolutely need the other feats here so you'll need to replace the other feats you've mentioned with them.
For the character’s weapons I chose two huge light crossbows to begin with.
Light Crossbows, contrary to their name, are not light weapons so you take a substantial penalty for two weapon fighting with them. You want to use Hand Crossbows, which have a specific exemption that lets them be treated as light weapons. Sadly, they're exotic weapons so you need to spend a feat on that.
I would put the impact enchantment on both and Agile enchanment on the offhand one so that I could add half dex to damage (since I'm unaware of another way to do this).
Impact and Agile can only be applied to melee weapons. Crossbows are not eligible to receive these enhancements. The only way to get dexterity to damage on Crossbows is by taking five levels of Bolt Ace.
Lastly, I would purchase a wand of gravity bow to increase the damage dice again.
Not worthwhile. Cast from a wand, Gravity Bow only has a 1 minute duration so you have a very short window of time to prebuff if you want the spell to stay in effect for combat, but the process of drawing your wand, using it, then stowing your wand takes at least 2 rounds. Leave buffing to the spellcasters in the party, don't waste your time and effort.
Here are my calculations for to hit:
You are correct that you have +11/+6/+1 base attack. From rapid shot you gain an additional attack at your full BAB, and from two weapon fighting you gain one attack at full and one attack at -5, so that gives you a base of +11/+11/+6/+1 with your main hand, and +11/+6 with your off-hand. For the sake of simplicity I'll presume you're using an identical weapon in both hands so we can just represent this as +11/+11/+11/+6/+6/+1
Now your modifiers. You have +6 from dexterity, -4 due to two-weapon fighting with a non-light weapon, -2 due to rapid shot, -3 due to deadly aim (I don't know where you're getting -5), -1 due to being a large-sized creature. I'm also presuming you should have an enhancement bonus on your weapon, so I'll give you +3 from that. That gives you a total modifier of -1
That gives you +10/+10/+10/+5/+5/+0 to hit. You are carrying way too many accuracy penalties here and will struggle to hit any monster with decent AC.
Deadly Aim does indeed seem quite risky here as the attack bonus severely decreases but if all the attacks would hit, then that’s a guaranteed 70 damage (since with a combined BAB of +18, the character qualifies for +10 to each damage per hit but at a -5 to hit to each attack). This may seem like quite a glass canon or very situational character if what I have calculated is true. However, his damage potential could be insane, especially since he was made with the intention of being a sniper hitman sort of character.
70 damage is actually pretty low. Let me show you a breakdown of a Fighter 6 / Bolt Ace 5 just off the top of my head:
24 dexterity (16 base +2 racial +2 level-up +4 enhancement)
Feats: Rapid Reload, Rapid Shot, Point Blank Shot, Precise Shot, Deadly Aim
Weapon: +4 Light Crossbow
Attack: +18/+18/+13/+8
Damage: 1d8+18
That's 90 damage average if everything hits, and with significantly higher accuracy. It also should be noted that I haven't even spent half my feats or picked up any Advanced Weapon Training options or archetypes for the Fighter. I also only counted the most basic equipment (dexterity-enhancing enhancing belt and a weapon) and haven't considered other helpful items. In other words, this is a skeletal build before optimization and customization.
(Attack breakdown: +4 to hit from weapon enhancement, +7 from dexterity, +1 from weapon training, -2 from rapid shot, and -3 from deadly aim for a total of +7 to hit.
Damage breakdown: +4 to damage from enhancement, +6 from deadly aim, +7 from dexterity, and +1 from weapon training for a total of +18)
Is this BROKEN?
No, dealing 100 damage per round if every attack hits is completely normal at the 11th level. Given your atrocious accuracy, it's actually on the weak side.
Also, don't take this too negatively. Your concept is cool and you've clearly done a lot of book delving to make it happen. However, always be mindful when you're taking double-edged options that have tradeoffs. On their own they aren't bad (Rapid Shot and Deadly Aim are staples for a reason), but if you're making three or four such tradeoffs you're going to fall very far behind someone who just takes the boring but efficient option every time.
*Glances in* I'm actually going to disagree with Dasrak on the appropriate level of damage for an 11th-level character.
The main thing to consider is this chart, which calculates the numbers a character will normally want to aim for at any given level.
I probably should have linked that chart, because it's a really good resource for getting ballpark numbers (although calculating EDV is a pain without a spreadsheet).
However, I have to wonder why you're disagreeing with me on 100 damage per round. That statement was presuming that everything hit, which is not what EDV is. If your highest iterative is an 18 (green rated) then your iterative attacks will be lower than this, and most of your attacks will miss against the benchmark AC of 25 for a CR 11 opponent. This means the raw 100 damage I was talking about earlier will have an EDV that's below 50. So yes, it's a completely normal amount of damage.
Well, mostly, I was disagreeing with the idea that "if every attack hits" is a measure that should be used.
That's the number that Gutsigrit was looking at, and I wanted to be clear that it's not an unusual number for that level range. I agree that damage must always be looked at in the context of the attack values that go along with it. EDV is a very precise measurement for that, whereas measuring the damage if everything hits then eyeballing your overall accuracy is a faster but rougher method.
A player in my emerald spire game had a similar idea. I poineed him towards Bolt ace 5/Alchemist 2-4, picking up the extra atm discovery twice. He uses one hand for a buckler and the other three for hand crossbows (Which Bolt Ace's Crossbow Maven gives you proficiency with).
I don't know his exact DPR, but dexterity mutagen and the bard's inspire courage help him to do a LOT of damage.