Braided lines have the banjos you order them with. The thread pitch doesn't matter to the lines, it matters for the caliper and master. As pictured, the Brembo RCS unit comes with the required double or single banjo if it's ordered correctly.
You should be ok with the fittings you have on your brake lines. The Corta Corsa RCS is different than the standard RCS but I believe the lines attach on the underside of the master in both cases. If you are getting new lines from Spiegler you'll need to us the tools they provide to rotate the fittings so the lines aren't twisted.
For bleeding new lines and a new master I like to get fluid to the calipers first. When I get fluid there, I will bleed the master so it pumps better. Basically, I open the bleeder and pull the lever then shut the bleeder before letting go of the lever. This prevents the master from trying to pull fluid/air back through the bleeder.
Your Corta Corsa is fancier than the standard RCS. It's got more adjustment. I picked up an RCS-17 Corta Corsa and don't quite know what I'm going to do with it yet. It was part of a package deal with a RCS-14 clutch master that's going on my KTM to match the RCS-14 brake master that I put on it.
Since Spiegler is providing replacement lines, you might be able to get them to put different fittings on the ends if you want them. I did an ABS bypass on my KTM and had them make full custom lines for it. I recommend talking to them about it since you've already got their ear for the replacements.