Travel between UK and Schengen area

As US citizen I am able to be here in UK for 180 days out of 360 days from my date of arrival. On Dec 7 I leave UK after being here for 176 days  I am traveling to Italy and Portugal -in Schengen area where I can be 3 months within a 6 month period.   

I need some clarification on how to best travel between Schengen area countries and UK or non-Schengen area over a 2 year period.
Can I be in Italy for one month, and then travel to Portugal for two months, then return to UK for three months, beginning a new 6 month stay in one year, and then return to  Italy for three months, and return to UK for three months?
When does the Schengen area (90 days within 180 days) start in the Italy?  Portugal?

I have heard that it is possible to be in a Schengen country for 3 months, stay in a non-Schengen area country for a few days and then, when I return to Schengen area it begins a new 6 month period.   Is this really possible?!

Any advice anyone can share with me on this will be extremely helpful.

The UK's 6 months in 12 rule applies to a rolling 12-month period not to calendar years. If you are in the UK June to December on a tourist visa and you try to return in March next year it is highly likely that you will be denied entry. You cannot use a tourist visa to live in the UK. Not sure about the Schengen rules.

THanks Bob for info on rolling year.    Actually I entered UK March 28 this year, was gone for 2 weeks short of 3 months so 180 days in UK is up for me on Dec 11. 
I need to know more about 90 days in 180 in Schengen area.  Is this possible - 90 days in one schengen country and then out of schengen area for a few days and then return to another Schengen country for 90 days?  I heard it is not mentioned, not promoted through official websites that one can return to a different Schengen country after a short stay out of schengen area and returning to another country.