You're spreading yourself thin on skills, with only 2 maxed out. Ideally your skills should be maxed, have only 1 rank, or none; 2-4 ranks on a level 5 character is usually a mistake. In particular escape artist is a skill to max or drop.
Gravity bow is not useful with a short bow. An effective +1 damage is not a good use of, at minimum, a standard action (to use the wand) and a move action (to draw it.) Aspect of the Falcon is still marginal but better, if you want an archery buff on a wand. Bless is worse for you than Aspect, but helps your party too.
On skills - as a true scholar I'd put one rank into every knowledge then max one. Likely the one you put a skill focus feat on. 14 spent.
Then max perception, disable device, UMD (remember, you can't take 10 on UMD - every point counts) and spellcraft. Another 20 makes 34 spent total.
Climb is a one rank skill, sure. With your last 6 skill points you choose one of linguistics, stealth and escape artist to put one rank into and one to put 5 ranks into, and drop whichever of these you didn't raise from your concept.
You haven't even specified which craft skill you have, so I'm assuming it's not important.
This would make you good at six skills rather than two and would keep almost every skill you've listed.
On your stats:
Archaeologists don't need that much Cha. The Bard spell list isn't very good on offensive spells, and you don't seem like you are making a casting focused character anyway. I'd switch your Dex and Cha around. How do you feel about dump stats? Wis can be dropped a bit for not a lot of damage, since Bards have good will saves. As a Half Elf, you can also trade your skill focus for Dual minded, which will help cover your will save.
I see that you are using your Skill focus for Eldritch heritage to get a familiar though. How much are you in love with having a familiar? Three feats is a lot to devote to it. It also delays your access to rapid shot and deadly aim, which are huge boosts to your ranged effectiveness.
On favored class bonuses: As a half elf, you have access to both human, elf, and half elf FCB's. Relevant FAQ. My suggestion: Take the Half elf bonus for three levels, until you get access to 2nd level spells, then stat taking the Human bonus, for more spells known. You will never regret having extra spells known.
As Revaar said bards do not make good offensive casters. Even if you are the only arcane caster in the group your spells will never really replace those of the wizard. What your spells are good for are utility and buffing. An archeologist is really a magical rogue. Get a CHA high enough to cast your spells and then put the rest into DEX. The familiar also does not do much for an archeologist and is significantly weakening your character by delaying other feats that are more useful.
One thing that works well for an archeologist is to go the dervish dancer route. Max out your DEX and use ancestral arms to get proficiency with scimitar. This will allow you to get DEX to hit and damage. Dervish dance combined with the archeologists other abilities often lead to him having the best chance to hit in the entire group. Archery is also a good way to go for combat but you do have options.
I would actually max out Disable Device, Perception and Stealth and put a single point into every other class skill. After you have a point in every class skill then you can start boosting other skills. Also make sure that heroism is you first second level spell. Heroism stacks with archeologist luck for some really high bonuses to everything. With Fates favored by 5th level you get a +5 to hit, saves and skills as well as +3 to damage. This combination is what really makes the archeologist shine. This also works on knowledge skills so you essentially have an additional +5 on all knowledge skills.
Also put every favored class bonus into extra rounds of performance. 30 rounds of luck seems like it should be enough for anything but if you are combining it with Heroism as I suggest you may need to burn through multiple rounds out of combat. Remember lingering performance means you have 10 uses of 3 rounds not 30 discrete rounds. If it takes a 5 rounds to sneak up on someone you just blew 6 rounds.
Make sure you have Expeditious Retreat and take Fast Stealth as your next rogue talent. This allows you to make stealth rolls while moving at 60’. Throw in invisibility on top of that and you are almost undetectable by almost anything. With a little luck you can even sneak up on things with the ability to detect invisible.
I understand where ur going and it's hard not to maximize dps but the group is already pretty dps oriented. I feel a familiar might prove to have a lot of utility and be enjoyable to play. Arcane bloodline does give other abilities as well including adding spells to ur known spells. I also figured if I could get to 22+ on cha with items I could have +2 lvl 2 spells per day.
You are the only arcane caster? I can see why you might be driven focus on the casting then.
As an alternative, might I suggest playing a Sage Seeker Sorcerer? You'd keep your handiness with traps, as well as having plenty of Skill points thanks to high Int, and you'll be able to support your party as a full caster.
Does your group already have a Bard who inspires courage? I ask because it seems like you are not really trying to get the most out of your Archaeologist's Luck. Archaeologist's Luck is all about boosting your personal DPR, but you aren't especially interested in boosting your personal DPR, since the rest of your party is already damage-heavy.
Archaeologist's Luck gets you a +3 +3 on all your attacks, with Fate's Favored. That's pretty good!
Regular Inspire Courage gives +2 +2 on everyone's attacks.
How can we compare those?
Well, +1 to hit is widely considered to be worth +2 on damage. So count your +3 +3 self buff as ((+3 * 2) +3) = +9 Attack Power. A buff of +2 +2 gives ((+2 * 2) + 2) = +6 Attack Power. But the whole-party buff applies to your whole party, so multiply it by five for a 4-man team plus one cohort (just a guess). So whole-party Inspire Courage +2 gives a total Attack Power bonus of (+6 * 5) = +30 Attack Power.
What this shows is that regular Inspire Courage Bardsong gives a whole party Attack Power bonus of +30, while Archaeologist's Luck gives a whole party Attack Power bonus of +9. That's more than 3x more effective, overall. So I hope you chose the Archaeologist archetype after determining that the party already has someone who does Inspire Courage. This basic mathematical reality is why Archaeologists are sometimes called 'selfish bards'.
Also, your weapon damage is wrong for your Longsword. You list it as +5 to hit for 1D8+1, when it should be +5 to hit for 1D8+2.
Since you are your team's only Arcane Caster it seems like you will be casting a lot of spells. You can't shoot your bow the same round you cast a spell. You also can't swing your longsword the same round you cast a spell. Ergo, you are unlikely to use either weapon very often, at least not until the outcome of a fight is decided and you switch to the conserving resources stage of the fight. This also means you won't be getting much benefit from your Archaeologist's Luck, as you will usually be casting a spell during the important early rounds of combat.
Suggestion: Consider buying and carrying a longspear as your primary weapon. The reason is that you sometimes can attack with a longspear on the same round when you also cast a spell. You do this by moving 15' away from a foe then you cast a spell. If the enemy wishes to move close and attack this provokes an AoO, giving you the attack you did not take during your round, to your benefit. If the foe does not choose to impale itself on your longspear then you are not being attacked, to your benefit. This is a passive aggressive way to inflict combat damage which does not consume actions during your turn. It's an ideal fighting style for a primary caster who also has basic martial competence, which you are and do. Also a longspear does more damage than a longsword, does not interfere with casting in any way, and surrounds you with a 25' diameter zone of protection that reduces incoming melee damage. Something to think about ...
Suggestion #2: Augment your +1 shortbow with a STR14 Composite Short Bow, if you can. Although +1 +1 is arguably worth 50% more than +0 +2, you eventually want both bonuses. Perhaps don't bother, though since you'll be casting so many spells you'll rarely have time for archery.
I disagree with the people who suggested possibly dropping your CHA to 14. As your team's only Arcane Caster, you'll probably be casting a lot of Grease and Glitterdust. I note you already have Grease. Perhaps consider replacing either Heroism or Gallant Inspiration, which are both buffs, with Glitterdust, your most powerful offensive spell. You want your spell DC as high as possible. Also, why is you INT so high? You already have a bazillion skill points, do you really need to boost your INT to get even more? Five extra HP are worth a lot more to you than 5 extra skill points, unless it's an especially easy campaign where your risk of death is already very low.
Bards are spontaneous spell casters so get very few spells. Unless this is a limited run campaign each spell should be one that will be useful at every level especially high level. Also avoid spells that can be duplicated with other abilities. Detect secret doors is not that useful past low level. As an archeologist you will have a really good perception roll. Abundant ammunition is not that useful once you get an efficient quiver. Don’t trade out heroism for anything it is just too useful, It can also be cast on other so you can use it to boost anyone in the party not just yourself.
If you want to cover some of the roles of a wizard/sorcerer consider going the illusions instead of combat spells. While they may not be that useful in a direct combat they can often avoid combat completely. Illusions also have the advantage that you only get a save if you interact with it. This means that even with the low save they can still fool people. For example if you cast a silent image over a door before anyone sees it the enemy may never search the area so gets no save. This will require some work on your part but can be very effective if done right.