I'm not able to see all my fields from my Unbounce form
When a new field is added to an Unbounce form, you'll need to publish the page and submit the new form at least once. Zapier will then be able to find a form submission that includes this new field.
The client isn't showing up in the dropdown to select when setting up a Zap.
Check your permission by Unbounce, as you must be the Author or Admin for a client in order to set up Zaps for it.