Problem:
It seems that there are translation options for normal posts/pages. But for all the custom posts/pages. There are no translation options at all. How to make them translatable?
Solution:
To be able to translate the custom post types, you need to set them as Translatable in the WPML settings. Please go to WPML > Settings > Post Types Translation section, then find the custom post type you want to translate and choose one of the two "Translatable" options.
Problem:
Custom Language switcher is not aligned with rest of the elements in the site.
Solution:
Custom language switcher is not expected to align automatically and the alignment depends on how your theme CSS is coded. Use Custom CSS to fix the alignment as required.
In this case the required CSS was, however this might not work for all sites: