Use Manage Display settings under 'Webform node type settings.'

It sure does, you get the default entity fields for the base form. I've never looked into whether the entity api has a way to put them inline... I doubt it... this could be pretty involved.

Also, marking this a feature request. Webform entity is intended to have a base form that behaves as an entity form by default, not like webform components. That said, I would very much like to add this feature.