Criminal law (StGB in .de) and rules relating to proceedings in crime-related investigations (StPO in.de) are not harmonized in the EU, so no, there is no EU law for this.
not much. EU hasn't got to the point to require strong citizen protections from law enforcement for whatever reason. UK is more similar to the US since uses a similar framework, but many accepted doctrines are quite different in EU even state by state, for example about the allowance of illegally obtained evidence