Are these related to Basque?
I am not a linguist, but I think not. I think Basque is sui generis or whatever the Basque phrase for one-of-a-kind is.
Are these related to Basque?
The majority linguistic opinion on Basque is indeed that it is sui generis, but some, such as Merritt Ruhlen in his book The Origin of Language, posit a relationship between Basque and languages as disparate as Georgian (Kartvelian), Ket (an obscure, nearly extinct language belonging to a "Yeniseian" language group, because its speakers live along the Yenisei river in Central Siberia), Navajo, and Chinese! (Cool, hunh?)
By the way, Ruhlen was a student of the late Joseph H. Greenberg, IMHO one of the greatest linguists of the 20th century, if not of all time, who posited a larger "super-family" of language families consisting of Indo-European, Finno-Ugric (Uralic), Altaic, and other more obscure languages, in his book "Indo-European and its Closest Relatives" published by Stanford a few years ago. Greenberg actually wasn't the first to propose a genetic link between Indo-European and Finno-Ugric, and the similarities between the Finno-Ugric (Uralic) and Altaic (E.g., TURKISH) language families are so prominent that they were noticed back in the 19th Century and led linguists to posit a "Ural-Altaic" group of languages.