Basque sagu 'mouse'

Basque sagu, sat- 'mouse' is a word found in compounds such as satandera (B, G), satandre (S, R) 'weasel' (and(e)re 'lady'), satitsu (G, HN) 'shrew' (itsu 'blind'), sat(h)or 'mole' (second member unknown) and saguzar (B, G) 'bat' (zahar 'old'), and which has cognates in Afrasian: Akkadian šikkû 'mongoose', Amharic ǝkokko (aškokko, ǝškokko) 'rock hyrax', Ge'ez sˁǝkˁ^wǝnkˁ^wǝn, sˁǝkˁ^wǝskˁ^wǝn 'field mouse; a kind of lizard'¹, Central Chadic *Sakw- 'squirrel; dog'², Omotic *sakw/*sikw 'chameleon; bat', Kartvelian *tsiqˀw- 'squirrel, mouse' (Georgian ciqˀwi 'squirrel'), Dravidian *tśikk- 'mouse', Old Turkish čekün 'young of marmot', Tungus čekše 'tarbagan (Marmota sibirica)'. Also related are Etruscan seχ³, Thracian súkhis and IE *dhug-h₂ter 'daughter'.

Although Bengtson links the Basque word to Caucasian *tsa:rggwɨ:(~ -ǝ:,-a:) 'weasel, marten' (see here), from which Starostin thinks the Kartvelian word was borrowed, in my opinion this is a genuine Eurasiatic root which in some languages (Kartvelian⁴, Dravidian, Altaic⁵) conflated with a phonetically similar word 'small'⁶, probably for tabooistic reasons. 

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¹ Quoted by Dolgoposky (ND 310a). See also W. Leslau (2010): Concise Dictionary of Ge'ez, p. 226.

² Where S is an unspecified sibilant.
³ Also spelled as sec, śec, śeχ. 

⁴ Kartvelian *tśˀukˀ- (Georgian cˀukˀ-an-a 'very small', Megrel čˀukˀ- 'mouse').

⁵ Altaic *tʃhjà:khe(~ -u) 'small'.

⁶ For which Dolgopolsky (ND 334) reconstructs a separated root, which he considers to be phonosymbolic. 

Basque begi 'eye' (updated)

Basque begi 'eye' is cognate to IE *s-meḱ- 'cheek, chin', as well as to Burushaski *-moq- 'face, cheek', with regular denasalization of initial *m-. This lexeme also appears as the second member of Nakh-Daghestanian *wimq’V 'witness; true' (NCED 2134), presumably a fossilized compound. 

By contrast, the Caucasian word for 'eye', *ʡwĭlʡi (NCED 34)¹, is reflected in IE *wel- 'to see' > Latin vultus 'face'.

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¹ Despite this, Starostin constructs from it a "Sino-Caucasian" etymology to which Bengtson links the Basque word.

Latin satellēs 'bodyguard'

Latin satellēs 'bodyguard', whose accusative satellite- was borrowed into French satellite, is a loanword from Etruscan zatlaθ 'axe-bearer', from zaθ, zat 'axe'¹. I think likely a connection with IE *h4adhes- 'axe, adze' (Hittite ates, atessa-, English adze, Latin assis, asser).

This formation is parallel to the theonym Raθlθ 'Stick-carrier', from raθ 'stick'², possibly related to IE *wraHd- 'root, branch' > Latin rādix 'root', a Wanderwort also found in Afrasian *rVhVt’- 'branch, rafter' (Semitic, Berber) and Georgian rt’o 'branch, bough'. Latin rāmus 'branch, bunch' < *wrād-mo- is cognate to Greek rhádamnos 'branch, twig', a Pre-Greek substrate loanword also found as rhódamnos, oródamnos.

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¹ Etruscan z stands for /ts/.

² Latin ratis 'rafter' must be an Etruscan loanword.