See the series by Walter Lee Sheppard, Jr.," Royal Bye-Blows, parts I, II, & III in the NEHGS Register (Apr 65, Jul 67, & Oct 68). See CP (Complete Peerage) VI:Appendix F, "Bastards of Charles II."; and vol. XI:Appendix D "Henry I's Illegitimate Children. You might also find a copy of Chris Given-Wilson, Alice Curteis, "The Royal Bastards of Medieval England," Routledge Kegan & Paul; (1988).
See also the online newsletter of the Richard III Society; specifically:http://www.r3.org/basics/basic5.html http://www.r3.org/basics/basic6.html
Lastly, if you can locate a copy, see ES (Europaische Stammtafeln) Band III Teilband II, " Band III Teilband 2, Nichtstandesgemasse und Illegetime Nachkommen der Regierenden Hauser Europas" for illegitimate children of European nobility.
As for your last question, yes both Richard III and Henry VIII were said to have had illegitimate children. Those of Henry VIII included: Henry, Duke of Richmond; Sir John Perot; (probably) Ethelreda, m. John Harrington; [?] Sir Henry Cary, Lord Hunsdon; [?] Sir Thomas Stucley. These names are from the above-mentioned article "Royal Bye-Blows," part II. Hope this helps.