Yeah, the timer though at the beginning made it clear they set a self-destruct.
Yeah.
Yup, it was strange there was no epilogue for Bruce about Alfred if Alfred really died like it seemed like.
They used a self-destruct on the cave and mansion. He's no doubt got plenty of money and accounts elsewhere.
I imagine they blew it up for full cover. It'll be the first place they take apart once he's "dead" now that they know he's Batman let alone whenever they get active so he had to get rid of the cave.
Alfred seemingly really dying seemed rather abrupt though.