Hello Henry,
many, many thanks for your help and your fast guidance on my two problems.
You’re absolutety right, the underscore was produced via the usual link hover effect. I added the second code snippet you provided and successfully got rid of the underscore. That’s a big yay!
Regarding the second problem: It could be, that the extra space is generated by the additional <span> around the email adress.
When I mark all the text in the sidebar with the three contact persons (https://ruoff-solar.de/unternehmen/engagement/) I can see where the extra space is located, it is directly after the email icon. This way the email adress is a bit more to the right then the phone number next to the phone icon.
Unfortunately I still don’t know how to fix this. But the more major problem is solved. Thank you, thank you, thank you!