Copy custom form and automatically copy custom fields?

Yes if you navigate to Setup > Custom Forms when you select a form you'll see the "Copy" button in the navigation. This allows you to make an exact copy of the form along with the fields and logic. It does not make a copy of the field but instead uses the existing field so any field edits will be reflected on all forms that use that field

Hi Lars ( @lgaertner ),

If you need the fields to be cloned so you'd end up with two fields (this could be seen as a potentially dangerous direction in that you could end up with a ton of custom fields and your list could get a little out of control) we don't currently have functionality that does that except perhaps via Fusion/API.  As @moniqueevans notes, current functionality will use pre-existing fields when you copy a form.  I would suggest adding this as an idea and cross-referencing it here if you decide you'd like to get community support for some variation of this need and for our product teams to consider it OR look to a Fusion scenario to address this unique need.

Thanks,

Ewan