I would prefer not passing as an expert and you understanding everything ;) I will clarify.
For the dash thing in the domain name, it can be fixed by using the canyoningallgäu.de domain as the main one. The pros of that is that your domain name will be better SEO (Search Engine Optimization) wise (it's best to avoid dashes all together and it's even better to avoid double dashes which are confusing to visitors). You can check Moving WordPress which will guide you the changing your WP address.
The double dashes also throws HTML5 validation errors which still let a visitor get a working copy of your site but you might end up penalized SEO wise.
For the <p> tags, the simplest option would be to use another slideshow plugin which will validate properly. It is a bad start for this plugin if the output is wrong.
The iFrame will be also taken care of by changing your slideshow plugin to a better one. Make sure you read other users review of the plugin in the WP repository.
Indeed, the dev tools are confusing at first. You'll need a basic knowledge of HTML and CSS to be able to use it properly but playing around with this tool is an incredible learning experience. With these suggestions, you shouldn't have to play around in the code to fix your issues.
I hope I made it easier to understand. Let me know if you need more help.