Does "minor revision" mean "accepted with minor revision"?
Yes, characterizing revisions as "minor" strongly suggests that if you make those revisions the paper will be accepted.  Editors may prefer not to explicitly say that the paper is "accepted with minor revisions", because authors may make "minor revisions" that don't correct the problems, and then feel that they've been promised publication in spite of that. 

Depending on the journal, the editor, and the revisions, the manuscript may or may not go out to re-review once again, and even if it doesn't a one-week delay from submission to re-evaluation is not surprising.  In my field (biology) I wouldn't be surprised to hear back about acceptance anywhere from 1 day to 1 month after re-submission.