Most or all of those questions have been answered at some point in time in this thread:
http://mersenneforum.org/showthread.php?t=20372
Of course, I couldn't tell you *where* in the thread the answers lie. Perhaps madpoo would have better luck refreshing our memories.
Suffice it to say, as Mark indicates, quad checks are surprisingly common, I think more than 10 per 1M exponent range, possibly even up to a hundred.
I think the most mismatches is somewhere around 6, though I may be recalling incorrectly.