GAP Analysis

Answer:
Customer facing services are explained in the following article:
ITIL Customer-facing vs. supporting services https://advisera.com/20000academy/blog/2014/05/27/itil-customer-facing-vs-supporting-services/
Additionally, I think that this article can help you with your concerns related to the customer facing services:
How ITIL can help reduce the gap between customers and the IT department https://advisera.com/20000academy/blog/2016/06/28/how-itil-can-help-reduce-the-gap-between-customers-and-the-it-department/

By supporting technology I assume you mean tool that is used for IT Service Management (ITSM). Please check the articles to get further information
5 things to beware of when selecting an ITSM tool :https://advisera.com/20000academy/blog/2016/03/08/5-things-to-beware-of-when-selecting-an-itsm-tool/
Free tools for ITSM – supporting IT Service Management for zero tool cost https://advisera.com/20000academy/knowledgebase/free-tools-for-itsm/

Regarding processes and their assessment - there are two issues. Firstly, you can measure GAP between existing processes and ITIL recommendations. ITIL GAP Analysis tool (https://advisera.com/20000academy/itil-iso-20000-tools/itil-gap-analysis-tool/) is suited for that purpose.
Secondly, you can go deeper and see how efficient processes are. For example:
How to measure Change Management efficiency according to ITIL https://advisera.com/20000academy/blog/2016/10/11/how-to-measure-change-management-efficiency-according-to-itil/
How to measure Incident Management efficiency according to ITIL https://advisera.com/20000academy/blog/2015/09/08/how-to-measure-incident-management-efficiency-according-to-itil/