thri-kreen secondary arms

If I create a thri-kreen fighter can I use the secondary arms to fight using two light weapons and the two-weapon fighting style while still using a shield on one of the primary arm's hand and holding a longsword or similar weapon in the other primary arm's hand?

Yes.

Your secondary arms can only wield Light weapons, but your primary arms can still wield any weapons and/or use a shield.

It should be noted that the extra arms do not, as written, give you any ability to make more attacks in a turn than you otherwise would.