Hey, I've had the same questions you do. Want to talk about it but everyone keeps saying "he's alive, he was at the cafe" and talking to me like I don't understand. Really they are the ones who don't seem to understand what I'm thinking. Here's my thoughts, they seem similar to yours...
I saw it the first time at the dark knight marathon and by three in the morning (and nine hours of Batman) I took the ending literal, I thought Bruce had faked his death Sherlock Holmes style. I didn't love the ending as much as I thought I would when that was my interpretation.
Then I saw it again Friday and was well rested and realized that Alfred in the cafe could just be his imagination. The shot glass he drinks seems to imply he is in despair and could fall prey to wishful thinking (I assume it was a shot glass but maybe it was espresso?, either way its not crucial to the point), also his reaction to seeing Bruce doesn't seem strong enough in comparison to his reaction at the funeral to speak to Bruce truly being alive. You think he'd have reacted stronger or longer at least before leaving. Also the fact that Bruce is with Selina having coffee, just as Alfred joked he should do earlier also speaks to this being Alfred's wishful thinking. *On the flip side I am aware people taking it at face value seem to think that Bruce did this purposefully as a nod to what Alfred said.
So I assumed that Bruce was dead for sure the second time. Then I saw the film for a third time on Saturday, despite the distress it caused my wallet. * I saw the film with different groups each time and depending on the group it really influenced my own interpretations the previous two times
The third time I realized that the ending is ambiguous. Without being able to rewind certain scenes it is hard to definitively tell but even once its on blu-ray and I can rewind, etc, it seems it may be more inception style than I had initially thought. I think the true genius of the film is that Goyer and Nolan set up the ending for both sets of people.
People who read into it all think Batman as Bruce gave his life. Alfred imagines things and 'Robin' takes his place as a new batman or new hero. People who just watch it at face value believe Bruce fakes his death to find a new life.
I think personally my interpretation is that Bruce died, but it was a far braver thing he did it at the end than the beginning because by the ending he was once again afraid to die. Another crucial shot is Batman in The Bat flying it after the smoke blast as he goes out into the water. For Bruce to have lived he would've had to jump out in that smoke blast and then the shot of him piloting the plane with only five seconds left is either a time cut or a lie (most face value people forget or ignore it all together). It seems more likely to me that the scene at the cafe is the 'lie' if you will. That he really pilots the plane and then Alfred imagines he sees him.
Other thoughts for that interpretation:
The auto pilot being fixed is just Bruce showing Lucious that he was making a willing choice, or also giving him hope that Bruce did survive or at least could have. Either way it shows him that Bruce's death was not a result of his busy schedule and lack of fixing the auto pilot.
The new bat signal could've been planted by Bruce before he died or could've been put there by the new batman, aka John Blake/'Robin'. Since Bruce did tell Blake to wear a mask but he didn't say which one. It seems odd that he would put the bat signal back up unless it was a sign that a new hero was out there or maybe the city put it in sort of the way they put up the batman statue. I would say Blake having it done makes sense, its another time cut thing where he does it after the batcave and decides he will be the new batman.
Ultimately this was a great film and each time I see it I love it more, its not as visceral as the second but realizing the genius of that ending and its multiple levels really upped this film for me, this is probably the smartest and most thought provoking film so far in the 21st century due to that ending (and of course I mean smartest and most thought provoking blockbuster or big budget film, and possibly will be the smartest ever because most big budgets go for the easy catharsis and spoon feed it to us).