Actually I should give more direct answers to the questions in the OP.
1-2) To the extent that an ideology helps someone make sense of the world, yes, one should have an ideology. I think a deliberate search for one is probably a waste in that respect - ultimately everyone makes sense of the world through their own experiences, and those experiences predispose them to particular ideologies. But inasfar as ideologies are simply observed patterns about the human experience, and recommendations for just action based on those patterns, they're useful tools for understanding the world and making it a better place.
3) Absolutely. Socioeconomic background and parental political affiliations are two of the strongest correlative variables to political identification in American society, and ostensibly neither of those should have much relevance to a conscious, deliberate search for the truth - which means that the circumstances into which one is born have a far stronger effect in biasing an individual toward a particular political outlook than you'd expect. I'd go far enough as to say that one's political outlook is largely deterministic, which means yes, most people have an ideology even if they don't know it.
4) One would hope, but I would sacrifice ideological consistency for... accuracy? I'm not sure what word I'm looking for here, but my first post in the thread alludes to it. An ideology is a heuristic (or series of heuristics) for understanding the world, and every time that heuristic fails you have to ask yourself if the failure rate is acceptable or not. If it is, you stick with it and own the errors where they occur. If it is not, you abandon it and find a better set of heuristics.