Should I roll the equivalent of 256 bits of entropy with a standard dice (# of rolls?), and sha256 hash it for the secret exponent?
You could, or you could write down each roll as a digit of a number in base(dice), then when you've rolled enough digits, simply use the resulting number as a private key itself.
What is a secure method for generating the bitcoin address from there?
You could just import the private key into Bitcoin-Qt. Then Bitcoin-Qt will tell you the address. For added security you could do this on a computer that is not, never has been, and never will be connected to the internet.
1. Is this a good approach?
It's a bit labor intensive, but sure, it'll work.
You could also leave the lens cover on a SLR camera, boost the ISO to the maximum setting available on the camera, and take a 30 second long exposure. The resulting noise in the image should be random, and have more than 256 bits. You could then SHA-256 hash the image for the private key. That's a lot less labor, and you could generate multiple keys/addresses pretty fast.
2. If I append "1", "2", "3" etc to the original series of rolls (seed).. does this constitute a "secure" method for generating a series of addresses?
Or perhaps just generate a single private key as a "seed" and then increment the value of the "seed" to generate a series of private keys? I'm not 100% positive, but I think that's how Eletrum handles deterministic addresses.