When database first is used, are the unique contraints added automaticly or they must be added manualy ?

UCs needed for 1:1 FK/UC - PK relationships are added when you click 'validate and adjust relational model data'. UCs you add to the entity are added as well automatically. So you can control the UCs from within the model

I mean this situation. I have a table in the database which has an unique contraint on a column. When I use the "Reverse engineer tables to entity definitions" function of the designer, the unique contraint won't show up in entity definition. Thus I cannot use the ConstructFilterFor function of the entity.

If it's defined on an FK, it won't show up as it's used to make the relationship 1:1. Also make sure you're using the latest build, I do recall there was a bug in an earlier v3 build for this.

It was because of the mentioned bug. I've got the new version and it works now fine.