Who could show me an example of the ending -κειμεν?

Well, this is a “late” (i.e. Koine) variant of the 1pl pluperfect active ending -κεμεν, as in “we had untied, ἐλελύ-κεμεν”. So you won’t likely get a Classical form.

The earliest instance I find is in Aristotle, Metaphysica 1041a:

καίτοι κἂν εἰ μὴ ἑωράκειμεν τὰ ἄστρα, οὐδὲν ἂν ἧττον, οἶμαι, ἦσαν οὐσίαι ἀΐδιοι παρ’ ἃς ἡμεῖς ᾔδειμεν

However, I presume that even if we had never seen the stars, none the less there would be eternal substances besides those which we knew

After that, it’s Josephus, Philo, Plutarch and Appian.

Why do Greek textbooks and paradigm references disagree on pluperfect endings, and how do I determine which are more standard for Attic vs Hellenistic?

If you want to go digging about this kind of thing, go digging in a German grammar. Dig in something that spends 300 pages on the different variants of verb ending.

Kühner–Blass, §213.5.

The original Pluperfect Active endings in the singular were -ea, -eas, -ee(n), which contract in Attic regularly to –ē, -ēs, -ein.

The variants –ein, -eis, -ein involved remodelling of the 1sg and 2sg endings after the 3sg ending –ein, and the middle aorist –ēn, -ēs, -ē. This first shows up in Isocrates and Demosthenes—so during the Classical period in Attic; that’s why you’re seeing both taught in grammars. The –ei– diphthong spreads to the Plural in “later” authors (that is, in the Koine: Aristotle, Plutarch); those are the endings you hesitate to consider “dubious” in details.

It’s hard for me to say which should be considered standard. A historically-oriented approach will go with the older endings, so those with the etas. And grammars of Classical languages tend to be historically-oriented. That’s what Smyth lists in its summary table (§383); the variant endings in Demosthenes are mentioned in passing in §701. For that matter, I’d be surprised if the teaching of Koine features the plurals in –ei– prominently.

Nick Nicholas: What’s the most unforgettable food that you have eaten in a foreign country?

Why is “damn” considered a dirty word while “condemn” is not?

Because, for better or worse, damn is what God does, and condemn is what a judge does. So damn picked up the religious and then blasphemous connotations which condemn never had, which made it much more eligible as a profanity. Profanity is all about the current taboos in society.

Are the many “i”-like combinations in modern Greek comparable to the “yat” and many “i”-sounding letters in old Russian orthography?

There is one major similarity between the Old Cyrillic and Greek alphabets: originally, both were (mostly) phonemic, but several of the distinct sounds represented by different letters merged later on, so that there was two or more ways of representing the same phoneme with different letters. So the letter Yat seems to have originally represented /æ/; its sound merged with /e/ in Russian, so that /e/ was written as both <Ѣ> and <е>.

In the same way, Greek for instance, used to have different pronunciations for <ω> and <ο>, /ɔː/ and /o/; Greek lost its quantity and quality distinctions, so to this day there are two ways of writing /o/: <ω> and <ο>.

On the other hand, the two different ways of writing /i/ in Old Cyrillic, <и> and <і>, were not comparable to Greek—they were inherited from Greek, where <η> and <ι> had already merged in pronunciation. Old Russian orthography had worked out rules for when to use one and when to use the other (Dotted I (Cyrillic) – Wikipedia); but those rules were artificial:

In the early Cyrillic alphabet, there was little or no distinction between the Cyrillic letter i (И и), derived from the Greek letter eta, and the soft-dotted letter i. They both remained in the alphabetical repertoire since they represented different numbers in the Cyrillic numeral system, eight and ten, respectively. They are, therefore, sometimes referred to as octal I and decimal I.

Are there reverse Latin and/or ancient Greek etymological dictionaries?

At a stretch, you could use Pokorny’s Indo-European dictionary to move forward, although it won’t move terribly much forward: you’d have to do the work of getting from Old English to Modern English yourself.

I’m not aware of such dictionaries myself, though I’d be surprised if someone hasn’t done one. These days, your best bet would be the text of an English Dictionary that allowed its etymologies to be searchable. Or, as Lotte Meester has pointed out, Wiktionary.

How did the Turkification of Byzantine empire take place?

I’m wondering how the old Greeko-roman culture of Byzantine, perhaps the most sophisticated in the middle ages, just collapsed and replaced by language and culture of tribal immigrant Turks who hardly had any written tradition?

For the specifics of what happened in Anatolia, see When and how did modern Turkish become the majority in Anatolia? (where I’m about to post an answer).

For the general principle: people don’t adopt a different language and culture because they’re choosing between Cyril of Alexandria and Avicenna, or between Michael Psellos and Ibn Tufail. People adopt a different language and culture because it will bring them direct benefit in their daily life, in the regime they happen to find themselves. And we’re talking a lot of peasants in Anatolia, who had never heard of Psellos or Cyril.

Is it true that most linguists assert Basque has not substantially changed?

Not to my knowledge. The late Larry Trask, preeminent vasconist of his time, spent a lot of leisure time refuting inane claims about Basque being related to every language on earth, and part of his armoury as a historical linguist was that such inane efforts made use of modern Basque dictionaries, whereas​ both what we have reconstructed of proto-Basque, and what little we know of Aquitanian, the ancestor of Basque, are phonologically different.

The word Ἀρσένιος (Arsenios) is latinized to Arsenius. Does the word θηλυκός (thēlykós) have a latinized form other than femina?

Bit of a misunderstanding here. The proper name Arsenius, Greek Arsenios (as in Arsenio Hall) is derived from the Greek word for ‘man’, arsen. But it was not the normal word for “masculine”, and LSJ records arsenios meaning “masculine” only once in a third century AD papyrus. The normal word for masculine was arsenikos (seemingly as in arsenic; in fact arsenic is from the Arabic al-zarnīq, which Greeks noticed sounded just like the Greek for “masculine”).

OP wonders, if the word for ‘masculine’ in Greek ended up in Latin, did the Greek word for ‘feminine’, thēlykos, end up in Latin as well? The Greek word for ‘masculine’ didn’t really end up in Latin, though, except as a name, and Google returns no hits whatsoever for +thelycus. So I’d be surprised if it did.