For the second round of peer review, the paper is usually sent to the same set of reviewers. So the second round is generally quicker than the first round of peer review as the reviewers are already familiar with the paper. A quick review and no request for further revisions indicate two possibilities:
1. The reviewers are satisfied with your revisions and your paper will probably be accepted.
2. The reviewers are completely dissatisfied and your paper will probably get a rejection.
Another possibility is that there is some delay in sending you the request for further revisions, and you will probably receive a mail from the editor about it in a few days.
Regarding your second question, I don’t think a request for “major revisions” decreases the chances of acceptance. A large number of manuscripts that receive a request for major revisions are accepted by journals after being revised. It all depends on how well you have revised your paper. If the reviewers are satisfied with your revisions, they will probably accept it.