The list of abilities you have listed (below) are all a pile of bonuses, and to keep it balanced, it will have to have drawbacks.
A way to tone this down while not leaving it out is to grant them a +8 bonus to climb checks, give them a climb speed equal to their base movement, and make climb always a class skill for the race. Another possibility is to grant the race immunity to web spells, flat out. In any case, it is a powerful ability that will need balancing.Spider Climb as spell (possibly either constant or limited uses per day)
Web as spell (limited uses per day)
Poison is powerful, especially as it should be based off of the CON ability modifier. Make sure it's clear that the attack provokes an attack of obbortunity unless Improved unarmed strike is taken. Even then it's still potent, when people WILL ask "Can I spit on my arrows?". At BEST, it would be 1d2 Dex primary and secondary.Paralytic poison bite
Remember, this opens up the Multi-attack line of feats.4 arms (2nd set half strength)
This one I disagree with. Composite eyes are not superior vision, just a different type of vision. With all of the above abilities, I'd leave this one out.Possible visual bonuses because of multiple eyes (bonuses spotting secret doors like elves or spotting illusions like gnomes)
NOW, to balance thr race out with those abilities, and these are all personal opinions:
Size: Small - Includes all the bonuses and minues of small size.
Ability score adjustments: STR -4, Dex +2, Con -2 (These are the size adjustment modifiers straight from the MM)
Natural Armor +2 (chitnin is a hard)
Cannot use Armor: Their bodies are just too complex to have any armor made for it.
Partial Vermin Subtype: Despite their high intelligence, they are still considered Vermin for the effects of many spells, such as repel vermin. However, due to their heightened intelligence, they are subject to the whole range of mind control spells.
A few more are needed, but I would need to know about the culture you have setup for them. Many of the core races abilities are based off of culture, as are their preferred classes.