Agur orori,
Hello:

> >> idu.......lay...................errun.......to lay eggs
>
> This Basque verb conforms to the pattern of Basque "infinitives"

(past participles / verbal adjectives, actually) with prefix e- and
suffix -n. According to Larry Trask, this type is historically
identical with the most common type e-VERB-i, for verbal roots ending
in -n

> (e-rrun-i > errui ~ errun).

Is this anything more than a simple hypothesis? BTW: *errui,
since "historically" -I and -N "participles" are NOT identical. And I
think this conjecture (that they're all one type) is rather weak.

> >> onritu....similar...............iruditu.....to resemble

> The Basque verb is actually irudi (some dialects add the verbalizer
> -tu < Latin -tu, -atu). Irudi itself, can be *e-rud-i or, more
> likely, a causative *e-ra-ud-i. The root is *ud or **dud/**lud.

1. I think rather improbable a -D verbal root (it'd be the only one
we know in Basque). In fact, thinking about this, I got more
convinced that the IDURI form might be the older one:
- it has an excellent parallel in EDIREN / ERIDEN, in whick -D-R-
is the older (cf. Old Biscaian edaraite < *edaro, and "modern" idoro).
- a -r root would be perfectly normal (cd -SUR- in isur 'pour')

If it were so (iduri), there would be no causative here. And
**dud / *lud.... nice ;-)

> The Basque word is haragi. The -gi part may be a suffix (cf.
> txerri-ki "pork, pig's meat", etc.)

Just a little help for next citations, you could better compare
with: gibel < *gi-bel, giharra / giharre < *gi-arre,...

> (kukula) The Basque word (with k-) cannot be ancient.

In fact, a K- word CAN be ancient in Basque, and it will usually
have a G- "partner" : koipe (and less widely used goipe), Old Alavese
kiltza / giltza, khur / gur (also present in makhur < *ma-kur, uzkur
< *utz?-kur,...), *kino > khio, khirats,....
Some originally G- words changed to K- (or developed K- partners)
after massive borrowings from Latin and Romance. But, of course, you
know this better than I do :-)

> Basque word is aho < *ano.

That aho comes from *ano is not so clear, is it? No nasalization in
Souletin nor in Roncalese, it might be just *aKo.

> There is no Bq. verb "ikan". To look is ikusi (root *kus)

To look is "beha", "so egin", "begira"; ikhus (*KUS) is just "to
see".

> uka- in compounds = underarm. Perhaps < *bugga.

I'm afraid it's just from UKHO / uko 'denial, refusal', and
probably ancient 'underarm'.

> Olatu "to wave". Ola = Spa. ola "wave"

No: olatu 'wave', as a substantive; nobody would use it as a verb.

> The Basque word for water is ur (**ud).

I'm really glad (and impressed!) to see Basque-X comparisons
treated so accurately and finely, we're used to rather nonsensical
searched of cognates in every language on the earth! Thanks :-))

P.S. Sorry for these rather off-topic commentaries ;-))