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- "search page" searching only Id value and not lib value (of course because it is the id value that is stored in EAClass object) i.e. I found pages, if I search "25_dgec" but not if I search "DGEC"

Yes, this is 'normal' because ATM only the raw value (id) is indexed for Database List properties.

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- Result "search page" displayed property name (and not the pretty name) FAQ have same issue. - my solr facet displayed my id value too.

Do you know how can I fix this issue (if someone understand my problem ;-) )?

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Here I paste a nice screenchot: http://snag.gy/Joa7q.jpg

ATM there's no solution for the search results highlights. The property name displayed there is part of the highlight (the matched text) and it cannot be parsed (if the property value is large enough and the match is somewhere at the end then the property name is not even included in the match).

To resolve the problem I use lib column to display correct value (and not the id)

Regarding the raw value (id) displayed in the facet, you can write a custom facet that displays the label corresponding to the raw value.

Yes I manage to did this solution, but I was confronted at multi class problem (again) Thxs anyway, I store pretty name in my Page with Class.