I have no idea why you don't get an on-screen keyboard when in portrait. Getting the on-screen keyboard in portrait is default behavior on my Pro1x with stock.
Yes, you install a Gapps package with Lineage (link in the Lineage instructions) and that gives you the Play Store.
I'm not sure with the default keyboard app, but I remember that SwiftKey gave me more flexibility there, including an options to get the correction line displayed even in landscape orientation together with the physical keyboard.