The Noctuary (D&D 3.5e, Level 20+ Adventure)

[chaincomplex]

Thrikreen (non psionic) I have as LA+1

The "Lesser" (Lesser section in PGtF p190)
Powerful Races at 1st Level portion
For each negative level adjustment, he takes the following penalties.

Can I apply the "Lesser" variant to this race?

Which variant? The one that's just an across-the-board negative level penalty will already be bought off by your XP. The lesser-race variant doesn't include thri-kreen.

Fire-Souled Template (DR314 p23) one source I show as LA+1, but the actual mag has this as LA+3
is acquired
I would like to know which way you rule it as?

+3.

are other turn attempts considered as turn undead, such as turn elementals?

I can't find a way to make the argument "yes" work by RAW interpretation, so no. It appears elemental turning is intended to be distinct from undead turning.