For my answer, I will use material from a 1931 article written to address this very issue: "The Use of Forem and Essem" by Winnie D. Lawrence, available on JSTOR.
While essem was always a good literary word, forem, after Plautus, gave evidence of decline in this respect. In later writers, especially in Sallust and Tacitus, it was an affected ...
In the beginning, way back in the far-flung times of Proto-Indo-European, the word for "it is" was something like *h₁ésti, and it had a fairly regular present participle, *h₁sónts. In Latin, these forms evolved into est and sōns, respectively (vowels get lengthened before -ns). The latter is where we get forms like absēns > "absent" and ...
To expand a little on Joonas's answer, the nominative singular ending in Latin was originally /os/ for all masculine nouns of the second declension, which developed to /us/ as part of a more general sound change of /o/ to /u/ in certain positions. (Somewhat confusingly, Latin /u/ in turn corresponds to /o/ in a number of Romance languages. It's thought that ...
It's not that esse takes the accusative—it's that cupiō takes the accusative, and esse links two things in the same case. In other words, regem is accusative because mē is accusative, and mē is accusative as the object of cupiunt.
This is a fairly common construction in Latin, called the "accusative with infinitive" (or accusativus cum infinitivō ...
Pinkster 2015 mentions the following observable trends regarding the omission of esse.
it is more frequent with the 3rd person than in the 1st or 2nd;
it is more frequent with present indicative forms;
it is more frequent in simple nominal sentences etc. (see pp. 201-204 for more details).
Stolz and Schmalz add that the omission of esse is regular in ...
It is servŏs in both instances, not servōs.
The old form of the nominative has the ending -os instead of the later -us.
What you see is indeed the singular nominative, but not in the form you are used to.
Indeed, it means [he] eats; it is a contracted form. It's not very common, nor extremely rare. Lewis & Short even call it "very frequent", which I think is an exaggeration:
The contr. forms es, est, estis, etc., are very freq. in prose and poetry: "est", Vergil, Aeneid 4, 66; 5, 683; Horace, Satires 2, 2, 57
My first instinct was that this is, at the very least, not common in classical Latin, and should only happen with participles that are basically adjectives and have lost some of their verbal semantics, like sapiens or patiens. The reason I think that, is that a present participle is perfectly capable of standing on its own in Latin, it doesn't need an actual ...
Yes to the first, usually no to the second.
In Latin, esse can almost always be dropped if the meaning is clear. This is even true when it's connected to another verb form, like in a perfect passive captus [est] or a passive periphrastic delenda [est].
Linguistically, this is called zero copula, and also appears in e.g. Russian. Consider also English ...
Cupere is a special kind of verb. You can use it to talk about something the subject of the sentence wishes to do himself. In that case you use an infinitive as the object and predicate nouns or adjectives are in the nominative:
Cupit rex esse.
He wants to be king.
Normal objects are in the accusative as usual, though:
Cupio placentam edere.
I want to eat ...
It's probably a coincidence.
Preface: My main source for this entire answer is The Origin of the Italic Imperfect Subjunctive by J. H. Jasanoff (Vandenhoek and Ruprecht, 1991). If this is contradicted by more recent scholarship, please feel free to correct me!
All but one of the example words given are in the second person singular, because this shows off ...
Es and este are the present imperative, esto and estote are the future imperative.
As far as I know, the difference between present and future imperatives is the same for all verbs, and esse is not different.
I think the general differences between present and future imperatives should be asked in a separate question — if not asked already.
It is not simply ...
Yes, it does happen.
The esse and the perfect participle need not be anywhere near each other.
For example, Cicero (in Verrem 2.1.16) writes:
In Siciliam sum inquirendi causa profectus.
The verb proficisci is deponent, but it doesn't invalidate the point.
The same freedom is found with other verbs as well (Pro Caecina 84.1):
…sum ex eo loco ...
Yes, you can.
In Latin you can always write ecce and a noun, as in ecce homo.
The infinitive of a verb (such as esse) can be used as a noun.
For oblique cases you would have to consider the gerund, but it is not needed here.
The phrase ecce esse will be a little difficult to parse, just as "lo, to be" is.
It is a compact and unusual expression, but I see ...
Omitting esse in future infinitives like facturum esse is very common and perfectly acceptable.
In fact, if something doesn't seem to quite make sense syntactically, it is often a good idea to check whether there could be an implicit est or esse somewhere.
I would consider conjunctive to be slightly more natural.
The decision in this sentence is subordinate ...
I think that the four examples from Ovid given by blagae are not quite relevant to the question raised by the OP: all of them can be argued to show a clearly adjectival behavior and are not infrequent at all in Classical Latin. It is not correct to say, as blagae does, that these examples "occur sporadically". One can apply the typical tests to ...
Esse could indeed be paired with a present participle, at least in Medieval Latin. Like Greek, this forms a periphrastic tense, which is pretty much the same as the English progressive, as far as I know. Similar to word order, its use was usually a matter of preference.