To completely remove the welcome banner, go to UI.X Welcome Block under style properties. Just tick off the show welcome block setting. We will be adding the option to hide it altogether in a future release.
As for the new/old badge, I believe all you need to go to is the Node Icons style property group and the first option is to nudge the left margin (increase it).
Yes, so go to UI.X Navigation style property group. There is a setting called Show Alerts Inline. Im on my phone or Id get you a screenshot. Then you can go and change the color to red if you want under Header and Navigation style property group.
Ah right. It's because the navigation is sticky. Disable navigation sticky and it will work. If the bubble pops off the pages while it is sticky the number will get cut off. Feel free to give it a try.
That's a shame though, is there no way to have both?
This is what I see if I turn Sticky Navigation off:
I suppose I would have to turn the user bar AND navigation to non-sticky for those flags to work as required? Not something I want to do as I love the sticky(ness) of those bars