my player wants exorcised elite advace from radicals. should i also apply "surviving possesion" effects from core?

Talk to your player about it, if that was what he wanted to have when he came up with the character concept. If you are in agreement, go right ahead. Purely RAW you do not apply the effects, but in the end its your game and you are the GM.

...Purely RAW you do not apply the effects...

How exactly did you came to this conclusion? Because nowhere in excorcised e.a. (in radicals handbook) authors state what is the relation between these efects.

For example in case of cryptos posession (disciples of dark gods p95) it is cleary stated that this is the differed mechanic and should not be stacket with core possesion-survining effects.

Best case for not stacking i came up with is that both core and radicals effets add 2d10 insanity points and applying them both seems redundant.

You pretty much answered that yourself, as the Radicals Handbooks makes no mention of the "Surviving Possession" effects it follows that the elite advance does not use any of the rules for it. With Elite Advances in general you only apply the rules given in thw Advance itself, and nothing else.