On point 2, the European Court of Human Rights (ECtHR, the court of the Council of Europe) blocked such deportations, etc. under the European Convention on Human Rights -- nothing to do with the EU.
The ECtHR is tasked with upholding fundamental freedoms like the Convention, the UN Charter of Rights, etc. and is completely separate from the EU.
"In May 2016, shortly before the EU referendum in the UK, the EU advocate general stated that the court was considering whether the European Court of Justice should adopt powers to rule on all cases of extradition of terrorists, a move described by analysts as ‘European Union power grab’ and rejected by most member States (Slack, 2016). The plan played into the hands of Brexit campaigners who used it to campaign against UK remaining in the EU with the former shadow home secretary David Davis (Now BREXIT minister) stating ‘The argument that Europe is somehow improving our security is falling apart in the Government’s hands’ (Slack, 2016). Thus, exit of the UK from the EU will make it easier for the country to deport foreign nationals, both EU and non-EU citizens, that could be of potential threats to the country."
The ECtHR is tasked with upholding fundamental freedoms like the Convention, the UN Charter of Rights, etc. and is completely separate from the EU.