Question 1: Most likely yes. The first editions of future volumes and future editions of current volumes will probably carry the Shonen Sunday banner. Same situation with Viz's publication of Black Lagoon; the first five volumes all had the V logo, but Vol.6, the first under the Signature line, sports the new "SIG" logo (you can see it in Vol.3 of 20th Century Boys and Vol.1 of Detroit Metal City).
Question 2: 110% No. Most likely future volumes of non-Viz produced Shonen Sunday titles will sport the Shonen Sunday logo, just like how One Piece - a Funimation title - also carries the Shonen Jump name and typesetting in its logo.
Wow. Viz is going go all-out on online manga. First IKKI and now Shonen Sunday. This is good as we can see more titles. And maybe, if these two online imprints succeed, we may see Shojo Beat be revived as an online-only title and Shonen Jump expand into producing online titles. Heck, it would be cool to actually get Claymore chapters every month legally and online instead of waiting over half a year for the next volume.