Hi LM, welcome to Englishforums.
(1) No, don't capitalize; the sentence is continuing. If it were
two sentences, it might look like this:
"Well, the thing is obvious," said John. "We won't be going there now."
Quotation marks and other punctuation don't mix very well, do they? To me, it's often a cosmetic question-- which way seems to show most clearly the association between parts?
(2) "He was a great man," said John.-- this is correct as it stands. Consider it one sentence, not completed until 'John'. Or consider that two periods will confuse the reader into thinking 'said John' is a sentence.
It also varies somewhat between Englishes and authorities. Try this link for more detail:
WEBSTER'S.