Alright, so as a summoner you can wear light armor so nab yourself a chain shirt. You might want to get yourself a crossbow because early on you run out of spells easy and you probably aren't built to hit things in the face.
The serpentine eidolon starts with 16 dex and +2 nat armor, so 15 ac total. If its small gets +2 dexterity(+1 modifier) and +1 to ac, making it a total of 17. The +2 good reflex is for reflex saves(diving out of an enemy's fireball). Your eidolons save DCs are usually half the eidolon's total HD(round down) + its constitution.
Your eidolon has 3 evolution points(is that your power points?) you spend on evolutions to shape it and give it powers. I would suggest going quadraped if you want some sort of dragon...(I don't know what beast your going for). You could for instance, spend 2 evolution points to grow a pair of arms, then spend another 1 to grow claws on those arms.
Theres a chart somewhere that has the bonus spells per day for having so much stats. Yours would be charisma. I think thats what your talking about right?
I don't know power points for summoners. Usually you follow the chart for 6 level spontaneous casting on the summoner's page and add in a bonus for your casting stat. Psionics use power points, but I don't know what rules your using.
I've never played a spell caster so I don't know what they "need" as per how to do spells, or what equipment.
They need a spell component pouch, a spare spell component pouch and a spell component pouch to give to another party member for safe-keeping. Anything else is optional, though weapons are considered useful and it's also a bit of a tradition to wear clothes.
How do I find my AC Modifier for my Serpent? Do my ability mods count for those saves ( IE 16 Dex = +3 mod, and "Good" save +2 = +5? )
No, your snake has it's own modifiers based on its own size, dexterity and whatnot.
Also, What is my "Ability Bonus" for my spells?
Charisma - it's what the Summoner's spellcasting "runs on", like Wisdom for a Cleric or Intelligence for a Wizard.
Also what are "Power Points"?
An optional system (psionics).
Yes, skilled is amazing. You can easily make a skillmonkey eidolon or sythesist. Perception is choice.
Yar.
We have a Humanoid Eidolon with somewhere around +16 (at level 6) Perception with no extra points in Wis.
I know some do very well with the Skill Monkey Eidolon who just use the Summon Monster Spell-Like Abilities for combat.
If you put a point into it, it can use sleight of hand, yes.