I found how to solve problem 2: It turned out there was a variable evil-cross-lines
. Setting this to t
simply solved that problem.
Together with the fix for vertical movement by PythonNut, here is the full solution:
;; Make movement keys work like they should
(define-key evil-normal-state-map (kbd "<remap> <evil-next-line>") 'evil-next-visual-line)
(define-key evil-normal-state-map (kbd "<remap> <evil-previous-line>") 'evil-previous-visual-line)
(define-key evil-motion-state-map (kbd "<remap> <evil-next-line>") 'evil-next-visual-line)
(define-key evil-motion-state-map (kbd "<remap> <evil-previous-line>") 'evil-previous-visual-line)
; Make horizontal movement cross lines
(setq-default evil-cross-lines t)