codestylist

Switch to a standard theme, like Twenteseventeen, and check again.
If the error disapears, you have to debug your theme.
By the way, to make CF7 compatible with Polylang you need an extra plugin (search for CF7 and Polylang in the plugin repository).

As @veerap wrote, you query always the en posts. You need to change the code
<?php query_posts('category_name=Introduction&lang='.pll_current_language()); ?>
You can find more about Polylang function here: https://polylang.wordpress.com/documentation/documentation-for-developers/functions-reference/

Deactivate all plugins except Polylang. Change to standard theme like twentyseventeen. Check if the error is still visible. If not, activate theme and plugins one by one and check which plugin is responsible for this issue.

As you said, this is a theme based translation. Polylang is for content translation. You can give Loco Translate a try.

I don’t believe the problem comes from Polylang. I use the plugin on a lot of sites and had never problems.
Did you also switch the theme to twentyseventeen?
You should run only a standard theme and Polylang plugin.
And, make sure you have also translated the main page and the pages (EN and NL) are linked together.

Deactivate all other plugins and switch to Twentyseventeen theme. Check if the error is still persist.
If not, activate the plugins and theme one by one and figure out which plugin or theme is producing the error.

This is CSS stuff and depends on your theme. Not possible to answer without the code.

This not part of Polylang.
You have to use Loco Translate and translate the Plugins language file. But, this will be overwritten with the next update.

Try to deactivate and activate the plugin. If this does not help, re-save permalinks.