Hi Witold, as well as psychological profile of migrants seen by themselves is quite important how they are treated by local people in their destinations. I would recommednt in such sense the recent researchnof IESA center in Andalucia region in Spain about the attitudes of people in relationship with immigrants. You can access to this study here (I attached the mentioned report to this message).
Hi. I think to estimate the psychological status and well-being of immigrants, suddenly, it would be important to take into account two levels of analysis: micro-analytical (the migrant subject) and macro-analytical (the structures in the host country).
Their level of satisfaction with the local integration structures, measured by the satisfaction with health and social services.
The opportunities in job mobility, the options of empowerment and development of their competencies, capabilities, economic authonomy, self-esteem.
Mental health (depressions, anxiety, lonelyness and other migratory troubles).
Relation withe their familiar, children, couple, the reunification, etc.
At the moment, this is my contribution. I hope it would be useful.