This is an older phrasing, unusual in the past few decades, especially in American English.
"Although he didn't care" is a good guess, but not quite right. Although, even though, and declarative+"still" mean that something did happen and it did not have the expected result. It would mean he had to do the opposite of what he wanted.
"Even were he not to care himself" means "Even if he didn't care himself." Even if, "even"+subjunctive, and subjunctive+"still" describe an imaginary situation (that did not happen) and would not have had the expected result. It can also describe an unlikely future situation that will not have the expected result. It means that he does care, but in the imaginary situation of not caring, he would have to do the opposite of what he wanted.
Here is an example with some alternate phrasings:
- Even had they offered her more money, she would've left the company.
- Had they offered her more money, she still would've left the company.
- Even if they offer her more money, she will still leave the company.
Here is a link to an excellent series of examples and explanations on using the subjunctive in similar ways:
http://www.bbc.co.uk/worldservice/learningenglish/grammar/learnit/learnitv342.shtml
OED's entry for the usage OP is concerned with says...
Intimating that the sentence expresses an extreme case of a more general proposition implied (= French même). Prefixed (in later use often parenthetically postfixed) to the particular word, phrase, or clause, on which the extreme character of the statement or supposition depends.
It also goes on to say...
This use, now the prevailing one in Eng., is foreign to the other Germanic langs. It is rare in purely dialectal speech, and (though a natural development of 8) seems not to have arisen before the 16th c.
(OED's definition 8 refers to a largely obsolete usage where even = ‘namely’, ‘that is to say’, ‘just’, ‘nothing else but’, ‘to be sure’, ‘forsooth’).
Note that although they're very similar in meaning, there's a slight distinction between...
1: She even forgot my birthday
2: She forgot even my birthday
In #1, it's implied she performed other different actions besides forgetting my birthday (maybe she ate my last Rolo, for example). In this case, even modifies the entire phrase forgot my birthday.
But #2 more specifically implies that she forgot other things (not necessarily even relating to me).
There's nothing at all "odd" about OP's "Will you even be there?" (it's emphasising that not only might you not do something when you're "there" - there's some question as to whether you will be there at all).
OP's "Who even is she?" and "What even is that thing?" are highly unlikely constructions that would probably be considered unacceptable/substandard by most native speakers. The reason for this is that even never really modifies the verb to be at all - it modifies whatever comes next, as in...
"Can't you even be polite?" (If you can't be/act how I want, can you at least be polite?).
"I can't even be bothered to reply" (I can't do much at all, specifically not bother to reply).
Best Answer
Sometimes, obeying rules that are falling into disuse has an intentional semiotic purpose. Lawyers, particularly, benefit from establishing that every word in their writing has been well-chosen, every sentence well-structured. Otherwise, a judge will be tempted to "interpret" what the writing "probably meant to say." (As an estates lawyer I know once put it, "If you want to get a court to read a will loosely, the first thing you do is piss on the will.")
The best inoculation against attack on a legal writing is obsessively, nay ostentatiously, correct grammar and usage. Accordingly, when I was lawyering, the more often I could correctly use "lay" and "lie" or "fewer" and "less" or "effect" and "affect" correctly, the more likely I was to be taken at my word. And, to the point, I never split an infinitive. Ever.
That said, there is a rule on the table: place the emphasizer ("even," here) closest to the entity of interest. But what constitutes and "entity"? "To consider" is a verb in its infinitive form." Thus, "to consider," and not "consider" is the "entity." Thus, the adverb "even" should be placed adjacent to the verb "to consider," not in the middle of it.
Arguably, "even" plus some other word(s) can constitute an entity. Phrases like "not even think about it" and "not even go there" may qualify. In those phrases, however, "not even .. about it" and "not even ... there" do not modify "think" or "go." Rather, the whole phrase is a single entity with no modifiers to place, so the infinitive form of the "verb" is "to not even think about it" or "to not even go there." Admittedly, as a lawyer, I prefer the "fiction" that these phrases are a single verb to which the rule against splitting infinitives applies to the notion that these expressions are "exceptions" to that rule. But maybe that's because I need rules to be inviolate so that I can make a show of not violating them...