Let's break these apart.
- Even if I do X, Y will happen.
- Even should I do X, Y will happen.
- Even if I should do X, Y will happen.
Even is being used as an adverb in all three cases, taking the second meaning in the Wiktionary listing:
"Implying an extreme example in the case mentioned, as compared to the implied reality."
So it is saying that "X" is one of the best options I have.
Numbers 2 and 3 are the same construction, where should is being used as an auxiliary verb to form the future subjunctive. This indicates that X is something I am only hypothetically interested in doing, just for the sake of argument. The indicative mood of number 1, by contrast, suggests that X is something I am actually interested in doing. However, in a conditional clause like this one, the difference between actual and hypothetical is quite small.
Edit: number 3 could possibly use a different meaning of should, that of obligation. In this case X is something I really ought to do, but instead of doing that I will do Y, something different. That's not really the meaning you are after, and might not be understood that way anyway, which is why I ignored it earlier.
In short, there is a fine distinction between the first example and the others, but for practical purposes you can treat them as the same.
I would interpret this anachronistic question as hipster-speak for:
So, what are your interests, employment, education, religion, and/or
life goals?
Basically this person is trying to determine whether you would make a valuable acquaintance or possibly sexual partner based on mutual interests.
Best Answer
It is roughly synonymous with the terms "not to mention" or "to say nothing of", except that those terms require a change in tense for the following action.
The sentence "I wouldn't go near a stingray, let alone pet one" implies that the speaker would stop far short of even being in a situation to do what follows the "let alone" clause. They wouldn't go near a stingray, therefore it is out of the question that they would pet one.