Worth pointing out that they can't make an application to the ECtHR until all legal appeals have been exhausted in the UK (Supreme Court?). Otherwise the application will be immediately rejected.
They do describe the route they are taking - they asked the government and got referred to the "Investigatory Powers Tribunal" (IPT) but the ECtHR has already decided that the IPT is a bit dubious so they may entertain a direct approach.
Depends. There have been cases in ECHR which didn't have national level court action first and drill succeeded, like the A B C v Ireland abortion ruling.
They'll do this the right way.