How do I stop unwanted emails from dating sites?

Use the Google Block Sender feature Block or unsubscribe from emails and Block or unblock peoples accounts, and in this case they also go to Spam. If using an Android device you can click on the three horizontal dots in Gmail app, to make similar Block/Unsubscribe settings.

How can I find out if my husband is on any dating sites?

Run a search using your spouses email address, name, phone number, and see what Google or any other search engine has to say about them. You can use Google images and search for your spouses profile photos that you can download from their social media accounts. They might show up in the search results.