C-J. Bailey explains such constructs with a virtual construct.
twenty past = twenty past seven that/this = that/this one/thing some = some body/one the good = the good folks (plural) are the good does = the good one (singular) does the greatest = the greatest one/thing those/these = those/these
(1) "Seven" is understood because it was just mentioned. I use the word "after" often in place of "past". (2) Yes, it's common to hear time given as "quarter after", "ten after", etc. when the hour is understood, especially if previously mentioned.