This one feels like the odd one out; all the other days seem to come fairly clearly from Latin (Sul-Sol, Llun-Luna, Mawrth-Mars, Mercher-Mercury, Iau-Ioue [spelling of Jove before J and V became discrete letters], Sadwrn->Saturn)...
...and then Gwener. Why didn't Venus end up as something like Finys?
Many words from Latin entered other languages not from the nominative form but from an oblique form - accusative or ablative or the like.
So the root here is not "Venus" but Vener- (as in "venereal disease", not "venusian disease" :D).
And Latin v- regularly turns into gw- in Welsh: gwin "wine" < vinum, gwyrdd "green" < viridis, etc.
Thus Vener- becomes Gwener.
Well, it might be due to a phonetic adaptation. Do the sounds "Ue-" (As we pronounce it in "Wait") or "Ve-", starting a syllable, exist in Welsh? Venus, in Latin, was formerly pronounced "Uenus" and afterwards "Venus". It is acceptable that, since Welsh didn't keep these sounds when latin was introduced in "Britania", they were replaced by "Gw-" the same way some french words were adjusted to english phonetic features (e.g. "Gua-" in Guarde-robe (garde-robe) has become "Wa-" in Wardrobe). What do you think?
I don't know, but if I drop the G of the beginning it reminds me of French vendredi or Italian venerdi
Yes: Venus (English comes from the nominative) -> Venerem (Romance come from the accusative) -> Gwener.
It is a common change that words beginning with U/W suffer. One other example is how the Germanic name Wilhelm became Guilherme/Guillermo in romance languages.
It sounds like the "dd" in "dydd" is being pronounced as a dull "th". Am I hearing that correctly?
A bit closer to "day of Frigga" or "Frigga's day", perhaps -- noun noun in Welsh is often a possessive along the lines of "the A of (a) B; an A's B", and with the definite article, noun y noun it becomes "the A of the B; the B's A", e.g. pobl y cwm which is "the people of the valley" and not merely "people the valley", and where the second noun is a proper noun such as personal name you have things such as llyfr Alys "Alice's book".
Though here, it's Venus's Day in Welsh (Gwener is from the oblique stem Vener- of Venus in Latin; compare Vener-eal disease), rather than Frigga's Day as in English. (Friday is worn down from frigedæg which is more transparently "Frigga's Day": Frige "Frigga's" is the genitive case of Frigu "Frigg(a)" so it would be something like Friggasday in modern English, perhaps.)