Items imported from Google Calendar appear automatically in your Daycast as mere suggestions, hence the lighter, faded look. Calendar items in this state aren't trackable, editable, or movable. They're also not visible to anyone but you.
To make a Google Calendar item part of your day plan, click the [+] icon to the left of the suggested item you want to add. Once accepted into your plan, it will look like any other task with the exception of the Google Calendar icon that appears in the far right of the task field. Like any other task, you'll be able to edit it, clock into it, and choose a project category for it. Teammates can see accepted calendar items if they browse to your plan, or if your clocked-in status reflects a calendar item.