Dear support,
We're receiving a lot of spam in Zendesk through the external contact form.
There is no way to mark tickets as spam for me. Is the functionality dependent on my account rights or just missing? Also, I cannot contact a live agent in any way. When using the Get help button on the website, I get stuck in a cyclical conversation with your support bot and there's no button to contact a real live person. I'm losing my mind here, please help.
It's definitely a little confusing -- you need to follow these steps inside your own Zendesk instance, you can't chat with Zendesk help on the main Zendesk site, even though that's backwards from how chat works for actual customers. Instructions here: https://support.zendesk.com/hc/en-us/articles/360026614173-Contacting-Zendesk-Customer-Support
For the spam thing, you'll want to make sure your Custom Role has permissions to delete and mark tickets as Spam. This is located at https://{yourdomain}.zendesk.com/admin/people/team/roles. You'll want to make sure this is checked for your role: 
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