Yup: Old Norse is kenna for "be familiar with, recognise"; Old English has cunnan for "know, be familiar with, know how to", whence "I can" (formerly "I know how to", now "I am able to"). Past participle couth, whence "uncouth*. Old English also has cnawan "to know" (also oncnawan, to recognise) from the same gno- root as Latin cognosco etc. -- whence "gnomic".
Again, yes: it's also Old Norse ek veit, Old English ic wat, Gothic ik wáit as in modern English "God wot". Wit and witness are also related to wisdom, all originally meaning "(I know because) I have seen", like the vidi of Caesar's veni, vidi, vici and, indeed, video as in 'games'
Also, interestingly enough: the gŵydd that @Toffidil referred to above is from this same video/vision root; and the GPC entry for adnabod gives an etymology that refers the syllable -na- back to the same -gno- root as 'know'.