Thank you for your questions. I am an expert in Immigration. As per the terms of Just Answer I am only able to give generic advice.
You have asked multiple questions and I will try and deal with them in light of the information provided by you.
1.do they share information about failed assylum claim between UK and EU? If so what sort of informations do they share. Does it automatically affekt my mothers visa to here? As your mother claimed asylum in the UK, the UK Government would have taken her fingerprints and biometrics. All EU states share this information. Please note that if you fail to disclose this information, depending what the law of that EU country is, they may consider it as deception for not disclosing it and may affect the outcome of her application. I would suggest that you speak to an immigration lawyer of the country you are considering applying for the visa for your mother.2.My sister is UK Citizen. Can she sponser my mother to uk? Your sister can sponsor her mother on a visit visa basis or can apply her to come to the UK permanently if your mother has serious medical condition. I have linked the relevant rules for your perusal:
Please note that any application you make, the UK Government will consider her past failed asylum claim.
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