What are the specific restrictions, regarding a convicted felon in the UK, after serving time and several years after the alleged offense, entering the United States to visit and possibly live at a certain juncture?

Depending upon the charge -you are probably inadmissible under Section 212 (2)(A)(I)(I) Crimes Involving Moral Turpitude or Section 212 (2)(B) 2 or more Criminal Offenses; of the INA. Persons charged under 2A1 and 2B would be inadmissible without a valid waiver of inadmissibility as a non-immigrant.

Contact the nearest US consulate for further details.

Just a quick point of contention: if you have been convicted and served time it is not an alleged offense. It is only alleged until innocence or guilt is established.