No, US citizens do not normally need a Schengen visa. They are normally allowed to stay for 90 days as a tourist without a visa.
You could spend only 90 days in the entire Schengen region. For a non-Schengen citizen, the Schengen region is like one nation from the perspective of visa requirements.
If you leave the Schengen area and go to a non-Schengen country, and then re-enter the Schengen area later, the "clock" starts again from zero. If you do not need a Schengen visa, this is an advantage. If you do need a visa, it is a disadvantage as you need to get a multiple-entry visa. So, if you plan in a trip outside Schengen in the middle of your travels, you can get 2 x 90 days. For example, if you are in France, you could do a trip to London, as the UK is not in Schengen.
As I understand it the Schengen agreement between EU countries allows free passage between the collaborating countries without the need to show passports. The UK does not participate as we don't trust the border controls of other countries. A US citizen travelling to a Schengen country needs to have the correct permit / Visa / whatever to visit that country and then will be free to visit all other Schengen countries.
Schengen visas are obtained from the embassy of the country you are first going to visit in the Schengen area.
Is the question: what countries does the US require a visa from? If so, the answer is that the US requires a visa from every country on Earth EXCEPT those member countries that are part of the Visa Waiver Program (VWP). However, even in these countries, those people with criminal records will STILL be required to obtain a visa.
You need to apply to the embassy of the first country you intend to visit in the Schengen Area.
Guam is a US Territory, and as such, just like any other US owned soil, a Visa is not required as long as you are a US citizen. Saipan also does not require a Visa to visit.
No, a visa is not necessary, as Japan is in the visa waiver program, but that would require an ESTA from you.
Americans do not need a visa to enter Costa Rica. Costa rican require a visa or green card to stay and work in US.
Most (if not all) countries require a visa for foreign visitors. Most of them have exceptions for citizens of certain countries. For instance a UK visitor does not need a visa to enter the US and vice versa. There are some countries where a US citizen can enter without a visa, and quite a few that require a visa for US citizens wanting to visit. It's best to ask at the consulate of the country you intent to visit, or ask at the authority in your country responsible for foreign affairs.
Assuming youre a UK citizen, you are no longer eligible for the Visa Waiver Program and would require a visa to visit the US. Moreover, the deportation record would make it difficult for you to get said visa, or even get residency in the US based on a marriage to a US citizen. If youre happy with never visiting the US, you should be fine.
Your question can only be answered if we know where you're going. Some countries require visas from US citizens, others do not.