Currently the Zendesk Submit a Request form doesn't have the ability for users to paste images, or format their question.
It's available for Agents and articles. For example, the "Submit a Request" page from Zendesk is just a text box. It should have full rich text support (respecting the setting in the admin interface).
We currently encourage our customers to not use the portal, but instead email where their formatting and inline images are preserved.
Plain-text Requests only
Rich Text Controls for Article Editing