Here are some more comments:
- I couldn't find a name for that phenomenon, besides euphonie.
- I think the only reason for this is euphonie, to avoid a difficult to pronounce combination of consonants.
- Grammatically you could form achetè-je, pesè-je, but those are IMHO never used, and instead we fall back on est-ce que j'achète, est-ce que je pèse ... but ...
- ... it is rarely done in practice, at least when speaking. The register would be pedantic, certainly when speaking. Also you cannot always use this construction in a meaningful way. Who would say dors-je? (now)? Also, if the inverted form is in an interrogative sentence, we would use est-ce que much more readily, certainly in conversation, and avoid this inversion.
- I would say it is fairly indistinguishable, and we think of the imparfait way before we realize it could possibly be a present with an inverted "-je".
- For the cases where the vowel used is é, although it's written with an é, it's definitely not pronounced like an é.
- We don't quite learn to form those expressions systematically in school. We encounter a few at some point probably in literature, but I would say that is about it. We can recognize them, but we might be hard pressed to make one.
- There is something funny going on withSome of these expressions are tied to a subjunctive (without the followingusual que we associate to the subjunctive?):
Puissé-je en finir avec cette histoire !
Je tiendrai jusqu'au bout, dussé-je en mourir.
Eussé-je ...
Namely, I have a hard time identifying which tense this would be if there was no inversion: does puissé-je correspond to je puis? But we don't use je puis anymore, we use je peux instead. How about dussé-je? We say je dois, and je dus would be a past tense, but a past tense here doesn't quite make sense. Moreover, dois-je sounds plausible too, so what exactly is this dussé-je? How about eussé-je? We could very well say ai-je, so this eussé probably does not correspond to ai. The closest it probably is to is the subjunctive que j'eusse, but we lost the que! Something more might be going on here than just appending a vowel for reasons of euphonie. In particular, the idea of wish or hope that is one function of the subjunctive is perceivable in dussé-je, puissé-je ..., but not in chanté-je, which is only factual.
So, I have a follow-up hypothesis that these expressions (or at least those tied to a subjunctive) could function more and more these days as ready-made formulas, in limited number, that we still see sometimes in print, but wouldn't use normally when talking, or even at all.